Sum Signed Graph

Title

Sum Signed Graph

Creator

Ranjith, Athira P

Contributor

Varghese, Joseph.

Description

A sum signed graph S = (G, f, and#963;) is a signed graph of the underlying graph G where f : V (G) and#8722;and#8594; {1, 2, . . . , | V (G) |} is a bijective function and and#963; : E(G) and#8722;and#8594; {+, and#8722;} is newlinea mapping such that and#963;(uv) = +, whenever f(u) + f(v) and#8804; n and and#963;(uv) = and#8722;, whenever f(u) + f(v) gt n. The minimum number of negative and positive edges among all the sum signed labelings of G is known as rna and rna complement number respectively. The maximum number of positive edges among all the sum signed labelings of G is known as adhika number. The set X and#8838; V (G) is said to be a s - dominating of a signed graph whenever X is a dominating set and there exists exactly s number of negative edges between X and its complement. The minimum cardinality of such a dominating set over all signed graphs of the graph G is called an s - domination number. newlineIn the present study, we initiate the study of a new labeling in signed graphs namely, newlinesum signed labeling. The characteristics of sum signed graphs and the bound of rna number of in terms of the number of vertices in the underlying graph are explored by examining the rna number of different graphs. The properties of signed graphs such as negating and balancing is analyzed. The relation between rna number and rna complement number is established. The connection of sum signed labeling with parity signed labeling and cordial labeling is discussed. The absolute cordial condition for graphs satisfying sum signed labeling is examined. The concept of s - domination was also introduced during this period of study. The s domination in both the positive and negative homogeneous signed graph is investigated for each value of s. The properties of s domination in sum signed graphs are also analyzed. The s - domination number for specifc values of s is investigated for various graphs. The maximum value of s for a graph for which the s - domination will exist is discussed.

Source

Author's Submission

Date

2023-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000252

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/519590