ON SOMBOR MATRIX AND ENERGY OF GRAPHS

Abstract

Let ζ(V, E) be a simple graph, with |V| = ρ and |E| = ϱ. The degree of a vertex vi ∈ V is the count of edges connected to vi denoted by ςi. The maximum(minimum) vertex and edge degree of a graph is denoted by ∆(δ) and ∆′ (δ′) respectively. A graph ζ is said to be complete if ∆ = δ = ρ − 1 denoted by Kρ. If a vertex set of a graph ζ is partitioned into two sets say |M| = υ and |N | = ν (partite sets) such that every edge meet both M and N then the graph is bipartite graph. If every vertex of M is adjacent to every vertex of N
then the graph is complete bipartite graph denoted as Kυ,ν. The graph K1,ρ−1 is called as star graph denoted by Sρ and the graph Kν,ν is called equi-bipartite graph. The complement of a graph ζ denoted by ζ is a graph defined on same vertex set as of ζ such that if two vertices are adjacent in ζ, then they are not adjacent in ζ. For more terminologies refer the following [1].