A survey of selected recent results on total domination in graphs - ScienceDirect Skip to main
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The domination number of a graph G is the smallest number of vertices which dominate all
remaining vertices by edges of G. The bondage number of a nonempty graph G is the …

In this paper we present a brief survey of bounds on selected domination parameters. We
focus primarily on bounds on domination parameters in terms of the order and minimum …

In this paper we characterized the dominating sets, total dominating sets, and secure total
dominating sets in the corona of two graphs. The secure total dominating sets in the join of …

A total dominating set in a graph G is a set of vertices of G such that every vertex is adjacent
to a vertex of the set. The total domination number γ t (G) is the minimum cardinality of a …

We prove the following result: If $ G $ be a connected graph on $ n\ge 6$ vertices, then there
exists a set of vertices $ D $ with $| D|\le\frac {n}{3} $ and such that $ V (G)\setminus N [D] …

A function f: V (G)→{− 1, 1} defined on the vertices of a graph G is a signed total dominating
function (STDF) if the sum of its function values over any open neighborhood is at least one …

Let G be a graph and G be the complement of G. The complementary prism GG of G is the
graph formed from the disjoint union of G and G by adding the edges of a perfect matching …

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent
to some vertex in S and if the subgraph induced by S contains a perfect matching. The …

A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to
some vertex in S. The total domination number of G, denoted by γt (G), is the minimum …