A subset D of ( ) V G is called an equitable dominating set if for every ( ) v V G D   there exists a vertex u D  such that ( ) uv E G  and | ( ) ( ) | 1 deg u deg v   . A subset D of ( ) V G is called an equitable independent set if for any , u D v   ( ) e N u for all { } v D u   . The concept of equi independent equitable domination is a combination of these two important concepts. ...

By the sorting method of vertices, the equitable chromatic number and the equitable chromatic threshold of the Cartesian products of wheels with bipartite graphs are obtained. Key–Words: Cartesian product, Equitable coloring, Equitable chromatic number, Equitable chromatic threshold

The paper is devoted to the combinatorial problem concerning equitable colorings of non-uniform simple hypergraphs. Let H = (V,E) be a hypergraph, a coloring with r colors of its vertex set V is called equitable if it is proper (i.e. none of the edges is monochromatic) and the cardinalities of the color classes differ by at most one. We show that if H is a simple hypergraph with minimum edge-ca...

A proper total-coloring of graph G is said to be equitable if the number of elements (vertices and edges) in any two color classes differ by at most one, which the required minimum number of colors is called the equitable total chromatic number. In this paper, we prove some theorems on equitable total coloring and derive the equitable total chromatic numbers of Pm ∨ Sn, Pm ∨ Fn and Pm ∨Wn. Keyw...

Let be a graph. If  , G V E    is a function from the vertex set   V G to the set of positive integers. Then two vertices are   G , u v V   -equitable if     1 u v     . 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, equ...