Co-even domination number of a modified graph by operations on a vertex or an edge

Articles in Press

Document Type : Original Article

Authors

¹ Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran

² Department of Mathematics, Technical and Vocational University, Tehran, Iran

Abstract

Let

G = (V, E)

be a simple graph. A dominating set of

G

is a subset

D \subseteq V

such that every vertex not in

D

is adjacent to at least one vertex in

D

. The cardinality of a smallest dominating set of

G

, denoted by

γ (G)

, is the domination number of

G

. A dominating set

D

is called co-even dominating set if the degree of vertex

v

is even number for all

v \in V - D

. The cardinality of a smallest co-even dominating set of

G

, denoted by

γ_{c o e} (G)

, is the co-even domination number of

G

. In this paper, we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph.

Keywords

Main Subjects