TITLE:
Graphs and Degree Equitability
AUTHORS:
Ahmad N. Al-Kenani, Nandappa D. Soner, Anwar Alwardi
KEYWORDS:
Equitable Domination Number; Equitable Path; Equitable Walk; Equitable Connected Graph; EquitableRegular Graph; Equitable Complement Graph; Equitable Cut Vertex; Equitable Line Graph
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.8,
August
5,
2013
ABSTRACT: LetG=(V,E) be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two verticesu, v ∈ V(G) areφ -equitable if｜φ(u)－φ(v)｜≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.