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On Circulant Completion of Graphs
A graph G with vertex set as {v0, v1, v2,.., vn-1} corresponding to the elements of Zn, the group of integers under addition modulo n, is said to be a circulant graph if the edge set of G consists of all edges of the form {vi, vj} where (i-j)(modn)?S?{1,2,,n-1}, that is, closed under inverses. The set S is known as the connection set. In this paper, we present some techniques and characterisations which enable us to obtain a circulant completion graph of a given graph and thereby evaluate the circulant completion number. The obtained results provide the basic eligibilities for a graph to have a particular circulant completion graph. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
On Combinatorial Handoff Strategies for Spectrum Mobility in Ad Hoc Networks: A Comparative Review
Technological advancements have made communication on-the-go seamless. Spectrum mobility is a networking concept that involves access technologies that allow highly mobile nodes to communicate with each other. Ad-hoc networks are formed between mobile nodes where fixed infrastructure is not used. Due to the lack of such fixed access points for connectivity, the nodes involved make use of the best network available to transmit data. Due to heterogeneous networks involvement, the mobile nodes may face trouble finding the most optimal network for transmission. Existing technologies allow the nodes to select available networks, but the selection process is not optimized, leading to frequent switching. This leads to packet loss, low data rates, high delay, etc. Many researchers have proposed optimal strategies for performing handoff in wireless networks. This paper reviews combinatorial strategies that make use of multiple techniques to perform a handoff. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
On degree product induced signed graphs of graphs
A signed graph is a graph with positive or negative signs assigned to edges. An induced signed graph is a signed graph constructed from a given graph according to some pre-defined protocols. An induced signed graph of a graph G is a signed graph in which each edge uv receives a sign (-1)|?(v)-?(u)|, where ?: V(G) ? ?. In this paper, we discuss degree product induced signed graphs and determine the structural properties of these signed graphs such as balancing, clustering, regularity and co-regularity. 2020 Author(s). -
On Degree Sequence of Total Graphs and the Order of the Graphs
In this dissertation we discuss about the degree sequence of total graphs of some general graphs. A total graph of G, denoted by T(G) has vertex set as the union of vertices and edges in G and vertices are adjacent in T(G) if they are adjacent or incident in G. We try to obtain the degree sequence of total graphs of particular graphs like complete graph, path, cycle, wheel and star, from the number of vertices of the given graph (without directly drawing the total graph). We also explain the decomposition of T(G) into G and K_(d_i )s where dis are degrees of each of the vertices in G, moreover discuss about the degree sequence of T(G)??T(Ge). -
On Equitable Chromatic Completion of Some Graph Classes
An edge of a properly vertex-colored graph is said to be a good edge if it has end vertices of different color. The chromatic completion graph of a graph G is a graph obtained by adding all possible good edges to G. The chromatic completion number of G is the maximum number of new good edges added to G. An equitable coloring of a graph G is a proper vertex coloring of G such that the difference of cardinalities of any two color classes is at most 1. In this paper, we discuss the chromatic completion graphs and chromatic completion number of certain graph classes, with respect to their equitable coloring. 2022 American Institute of Physics Inc.. All rights reserved. -
On equitable chromatic topological indices of some Mycielski graphs
In recent years, the notion of chromatic Zagreb indices has been introduced and studied for certain basic graph classes, as a coloring parallel of different Zagreb indices. A proper coloring C of a graph G, which assigns colors to the vertices of G such that the numbers of vertices in any two color classes differ by at most one, is called an equitable coloring of G. In this paper, we introduce the equitable chromatic Zagreb indices and equitable chromatic irregularity indices of some special classes of graphs called Mycielski graphs of paths and cycles. 2020, SINUS Association. All rights reserved. -
On Equitable Near Proper Coloring of Certain Graph Classes
The non-availability of sufficient number of colors to color a graph leads to defective coloring problems. Coloring a graph with insufficient number of colors cause the end vertices of some edges receive the same color. Such edges with same colored end vertices are called as bad edges. The minimum number of bad edges obtained from an equitable near proper coloring of a graph G is known as equitable defective number. In this paper, we discuss the equitable near proper coloring of some families of graphs and we also determine the equitable defective number for the same. 2022 American Institute of Physics Inc.. All rights reserved. -
On equitable near proper coloring of graphs
A defective vertex coloring of a graph is a coloring in which some adjacent vertices may have the same color. An edge whose adjacent vertices have the same color is called a bad edge. A defective coloring of a graph G with minimum possible number of bad edges in G is known as a near proper coloring of G. In this paper, we introduce the notion of equitable near proper coloring of graphs and determine the minimum number of bad edges obtained from an equitable near proper coloring of some graph classes. 2024 Azarbaijan Shahid Madani University. -
On Equitable Near Proper Coloring of Mycielski Graph of Graphs
When the available number of colors are less than that of the equitable chromatic number, there may be some edges whose end vertices receive the same color. These edges are called as bad edges. An equitable near-proper coloring of a graph G is a defective coloring in which the number of vertices in any two color classes differ by at most one and the resulting bad edges is minimized by restricting the number of color classes that can have adjacency among their own elements. In this paper, we investigate the equitable near-proper coloring of Mycielski graph of graphs and determine the equitable defective number of those graphs. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
On equitable near-proper coloring of some derived graph classes
An equitable near-proper coloring of a graph G is a defective coloring in which the number of vertices in any two color classes differ by at most one and the bad edges obtained is minimized by restricting the number of color classes that can have adjacency among their own elements. This paper investigates the equitable near-proper coloring of some derived graph classes like Mycielski graphs, splitting graphs and shadow graphs. Jose S., Naduvath S., 2022. -
On families of graphs which are both adjacency equienergetic and distance equienergetic
Let A(G) and D(G) be the adjacency and distance matrices of a graph G respectively. The adjacency energy or A-energy EA(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of A(G). Analogously, the D-energy ED(G) is defined to be the sum of the absolute values of the eigenvalues of D(G). One of the interesting problems on graph energy is to characterize those graphs which are equienergetic with respect to both the adjacency and distance matrices. A weaker problem is to construct the families of graphs which are equienergetic with respect to both the adjacency and distance matrices. In this paper, we find the explicit relations between A-energy and D-energy of certain families of graphs. As a consequence, we provide an answer to the above open problem (Indulal in https://icgc2020.wordpress.com/invitedlectures, 2020; http://www.facweb.iitkgp.ac.in/rkannan/gma.html, 2020) The Indian National Science Academy 2022. -
On ideal sumset labelled graphs
The sumset of two sets A and B of integers, denoted by A + B, is defined as (formula presented). Let X be a non-empty set of non-negative integers. A sumset labelling of a graph G is an injective function (Formula Presented) such that the induced function (Formula Presented) is defined by (Formula presented). In this paper, we introduce the notion of ideal sumset labelling of graph and discuss the admissibility of this labelling by certain graph classes and discuss some structural characterization of those graphs. 2021 Jincy P. Mathai, Sudev Naduvath, and Satheesh Sreedharan. This is an open access article distributed under the terms of the Creative Commons License, which permits unrestricted use and distribution provided the original author and source are credited. -
On Improving Quality of Experience of 4G Mobile Networks A Slack Based Approach
This paper analyses Indias four top 4G Mobile network Providers with respect to five key user experience metrics Video, Games, Voice app, Download speed and Upload speed. Results using Data Envelopment Analysis show Airtel and Vodafone-Idea performing with maximum relative efficiency with respect to these metrics, while BSNL and Jio closely follow them. Further analysis using the Slack Based Measure shows where and by how much BSNL and Jio need to improve to perform at par with Airtel and Vodafone-Idea. On certain variables, for instance Voice app, BSNL and Jio perform well, with no need for improvement. On the contrary, for Upload and Download speed experiences, both BSNL and Jio lag. For Video and Games, there is still scope for improvement, although both these players are reasonable in their performance. Thus, this analysis provides an accurate and optimal benchmark for each variable whose user experience has been evaluated. 2021, Springer Nature Switzerland AG. -
On interval valued fuzzy graphs associated with a finite group
We associate a particular type of interval-valued fuzzy graph(IVFG) called interval-valued fuzzy identity graph(IVFIG) with every finite group and study its various properties. We show that IVFIG associated with a finite group is not unique. We also show that every IVFIG associated with a finite group is a strong IVFG. It does not contain any feeble or weak arcs. Further, it is strongly connected. We prove that the IVFIG associated with a finite group in which every element is self inversed is an interval-valued fuzzy tree and the IVFIG of Zn (n is odd) under addition modulo n is the disjoint union of interval-valued fuzzy cycles. 2020 Author(s). -
On ion transport during the electrochemical reaction on plane and GLAD deposited WO3 thin films
Tungsten oxide thin films were deposited on FTO and Corning glass substrates on Plane and GLAD (75) using DC magnetron sputtering and characterized using SEM, XRD, UVVis spectrophotometer, and Electrochemical analyzer systematically. Further, a comparative analysis was carried out in which it was observed that the result of surface morphology for plane showed the denser and GLAD showed nanopillars deposition. The amorphous nature of the sample was evident from XRD analysis. Optical transmittance was between 87% and 81% for both plane and GLAD. The Electrochemical studies showed the diffusion coefficient of H+ ions are more compared to Li+ ions for both plane and GLAD and Coloration efficiency was calculated at the scan rates of 10, 30, and 50 mV/s at the wavelength of 500 to 600 nm. 2021 -
On J-Colouring of Chithra Graphs
The family of Chithra graphs is a wide ranging family of graphs which includes any graph of size at least one. Chithra graphs serve as a graph theoretical model for genetic engineering techniques or for modelling natural mutation within various biological networks found in living systems. In this paper, we discuss recently introduced J-colouring of the family of Chithra graphs. 2020, The National Academy of Sciences, India. -
On L? (2, 1)-Edge Coloring Number of Regular Grids
In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative integers. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. We find the edge coloring number of these grids to be 9, 7 and 16, respectively so that we could color the edges of a rectangular, hexagonal and triangular grid with at most 10, 8 and 17 colors, respectively using this coloring technique. Repeating the sequence pattern for different grids, we can color the edges of a grid of larger size. 2019 D. Deepthy et al. -
On l(T, 1)-colouring of certain classes of graphs
For a given set T of non-negative integers including zero and a positive integer k, the L(T, 1)-Colouring of a graph G = (V, E) is a function c: V(G) ? {0, 0, , k} such that |c(u) ? c(v)| ? T if the distance between u and v is 1 and |c(u) ? c(v)| ? 0 whenever u and v are at distance 2. The L(T,1)-span, ?T,1(G) is the smallest positive integer k such that G admits an L(T, 1)-Colouring. In this article we initiate a study of this concept of L(T, 1)-Colouring by determining the value of ?T,1(G) for some classes of graphs and present algorithms to obtain the L(T, 1)-Colouring of paths and stars. 2020 IJSTR. -
On Leech labelings of graphs and some related concepts
Let G=(V,E) be a graph and let f:E?{1,2,3,} be an edge labeling of G. The path weight of a path P in G is the sum of the labels of the edges of P and is denoted by w(P). The path number of G, tp(G) is the total number of paths in a graph G. If the set of all path weights S in G with respect to the labeling f is {1,2,3,,tp(G)}, then f is called a Leech labeling of G. A graph which admits a Leech labeling is called a Leech graph. Leech index is a parameter which evaluates how close a graph is towards being Leech. In this paper, the path number of the wheel graph Wn is obtained. We also determine a bound for the Leech index of Wn and a subclass of unicyclic graphs. A python program that gives all possible Leech labelings of a cycle Cn for n?3, if it exists, is also provided. 2023 Elsevier B.V. -
On m-quasi Einstein almost Kenmotsu manifolds
In this article, we consider m-quasi Einstein structures on two class of almost Kenmotsu manifolds. Firstly, we study a closed m-quasi Einstein metric on a Kenmotsu manifold. Next, we proved that if a Kenmotsu manifold M admits an m-quasi Einstein metric with conformal vector field V, then M is Einstein. Finally, we prove that a non-Kenmotsu almost Kenmotsu (?,?)' -manifold admitting a closed m-quasi Einstein metric is locally isometric to the Riemannian product Hn+1Rn, provided that ?-?(2n+m)/2m = 1. 2021 Universita degli Studi di Parma. All rights reserved.