STRONG AND WEAK DOMINATION OF MIDDLE GRAPHS OF PATH AND CYCLE GRAPHS

Abstract

Let G =(V,E) be a simple, finite, undirected and connected graph. Let then strongly dominates v if (i) and (ii) .A non empty subset is a strong dominating set (sd-set) of G if every vertex in is strongly dominated by at least one vertex in S. Similarly, a weak dominating set (wd-set) is defined. The strong (weak)domination ᵞs (ᵞw) number of G is the minimum cardinality of a sd-set (wdset). The middle graph M(G) of a graph is obtained by subdividing each edge of G exactly once and joining all these newly added middle vertices to the adjacent edges of G. Let denote the greatest integer not greater than and denote the least integer not less than . In this paper, we investigate the strong and weak domination number of the middle graphs of the path Pn and the cycle Cn .
AMS Subject Classification: 05C09.