February 9, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

Research

Title Global outer connected domination number of a graph
Type Article
Keywords
Global domination, outer connected domination, global outer connected domination, trees.
Journal Algebra and Discrete Mathematics
DOI It does not have DOI
Researchers Morteza Alishahi (First researcher) , Doost Ali Mojdeh (Second researcher)

Abstract

For a given graph G = (V,E), a dominating set D ⊆ V (G) is said to be an outer connected dominating set if D = V (G) or G−D is connected. The outer connected domination number of a graph G, denoted by e c(G), is the cardinality of a minimum outer connected dominating set of G. A set S ⊆ V (G) is said to be a global outer connected dominating set of a graph G if S is an outer connected dominating set of G and G. The global outer connected domination number of a graph G, denoted by e gc(G), is the cardinality of a minimum global outer connected dominating set of G. In this paper we obtain some bounds for outer connected domination numbers and global outer connected domination numbers of graphs. In particular, we show that for connected graph G 6= K1, max{n − m+1/2 , 5n+2m−n^2−2/4<= gc(G) <=min{m(G),m(G)}. Finally, under the conditions, we show the equality of global outer connected domination numbers and outer connected domination numbers for family of trees.