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Doost Ali Mojdeh

Doost Ali Mojdeh

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Phone: 011-35302448

Research

Title
Global outer connected domination number of a graph
Type
JournalPaper
Keywords
Global domination, outer connected domination, global outer connected domination, trees.
Year
2018
Journal Algebra and Discrete Mathematics
DOI
Researchers Doost Ali Mojdeh ، Morteza Alishahi

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.