A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number t(G).â€¦ (More)

A set S of vertices is a total dominating set of a graph G if every vertex ofG is adjacent to some vertex in S . A paired-dominating set of G is a dominating set whose induced subgraph has a perfectâ€¦ (More)

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating ifâ€¦ (More)

A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class. We present new boundsâ€¦ (More)

In a graph G= (V , E) of order n and maximum degree , a subset S of vertices is a k-independent set if the subgraph induced by S has maximum degree less or equal to k âˆ’ 1. The lower k-independenceâ€¦ (More)