A total dominating set of a graph G=(V,E) is subset D V such that every vertex in adjacent to at least one D. The domination number G, denoted by ?t(G), the minimum cardinality G. near-triangulation biconnected planar admits plane embedding all its faces are triangles except possibly outer face. We show this paper ?t(G)??2n5? for any G order n?5, with two exceptions.

For a graph G=(V,E), we call subset S?V?E total mixed dominating set of G if each element V?E is either adjacent or incident to an S, and the domination number minimum cardinality G. In this paper, initiate study connected by giving some tight bounds in terms parameters such as order numbers its line graph. Then discuss on relation between diameter. Study trees 2-corona graphs our next work. Al...

In this paper we introduce the concept of strong total domination in fuzzy graphs. We determine the strong total domination number for several classes of fuzzy graphs. A lower bound and an upper bound for the strong total domination number in terms of strong domination number is obtained. Strong total domination in fuzzy trees is studied. A necessary and sufficient condition for the set of fuzz...