TOTAL AND CONNECTED DOMINATION IN CHEMICAL GRAPHS

Abstract

For a given graph G a subset D of the vertex-set V (G) of G is called a total dominating set if every vertex v ∈ V (G) is adjacent to at least one vertex of D.  The total domination number γ_t(G) is the cardinality of the smallest total dominating set.  Also D is called a connected dominating set if every vertex v ∈ V (G) − D is adjacent to at least one vertex in D and the induced subgraph ⟨D⟩ is connected.  The connected domination number γ_c(G) is the minimum cardinality taken over all connected dominating sets of G.  In this paper, we determine the domination number, the total domination number and the connected domination number for some chemical graphs.