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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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 certain topological indices of signed graphs
The first Zagreb index of a graph G is the sum of squares of the vertex degrees in a graph and the second Zagreb index of G is the sum of products of degrees of adjacent vertices in G. The imbalance of an edge in G is the numerical difference of degrees of its end vertices and the irregularity of G is the sum of imbalances of all its edges. In this paper, we extend the concepts of these topological indices for signed graphs and discuss the corresponding results on signed graphs. 2020 the author(s). -
On Certain J-Colouring Parameters of Graphs
In this paper, a new type of colouring called J-colouring is introduced. This colouring concept is motivated by the newly introduced invariant called the rainbow neighbourhood number of a graph. The study ponders on maximal colouring opposed to minimum colouring. An upper bound for a connected graph is presented, and a number of explicit results are presented for cycles, complete graphs, wheel graphs and for a complete l-partite graph. 2019, The National Academy of Sciences, India. -
On certain chromatic topological indices of some Mycielski graphs
As a coloring analogue of different Zagreb indices, in the recent literature, the notion of chromatic Zagreb indices has been introduced and studied for some basic graph classes in trees. In this paper, we study the chromatic Zagreb indices and chromatic irregularity indices of some special classes of graphs called Mycielski graphs of paths and cycles. 2020 Yarmouk University. All rights reserved. -
On C-Perfection of Tensor Product of Graphs
A graph G is C-perfect if, for each induced subgraph H in G, the induced cycle independence number of H is equal to its induced cycle covering number. Here, the induced cycle independence number of a graph G is the cardinality of the largest vertex subset of G, whose elements do not share a common induced cycle, and induced cycle covering number is the minimum number of induced cycles in G that covers the vertex set of G. C-perfect graphs are characterized as series-parallel graphs that do not contain any induced subdivisions of K2,3, in literature. They are also isomorphic to the class of graphs that has an IC-tree. In this article, we examine the C-perfection of tensor product of graphs, also called direct product or Kronecker product. The structural properties of C-perfect tensor product of graphs are studied. Further, a characterization for C-perfect tensor product of graphs is obtained. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.