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Abstract

A total dominating set of a graph G is the dominating set P of G, i.e. there is no isolated vertex in the sub graph triggered by P, where W is the set of vertices of G, that is, each peak in W (G). Each u ∈ P is said to be a (total) dominant set if P \ {u} is not a (total) dominant set. The upper total dominant number Γt (G) and the upper dominant number Γ(G) are the maximum cardinality of a minimal total dominating set and a minimal dominating set of G respectively. For each graph without isolated vertices, Γt (G) ≤ 2Γ (G). In this paper, we solve this problem namely, the nature of sub cubic graphs that satisfy, by generating a set of sub cubic graphs, which we call triangle-trees. We solved that the combined cube graphs satisfy G by.

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