A survey of selected recent results on total domination in graphs - ScienceDirect Skip to main
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A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a
vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as …

A set D of vertices in a graph G is a paired-dominating set of G if every vertex of G is
adjacent to a vertex in D and the subgraph induced by D contains a perfect matching (not …

For a graph G, the k-total dominating graph D_ {k}^{t}(G) is the graph whose vertices
correspond to the total dominating sets of G that have cardinality at most k; two vertices of D …

Nordhaus–Gaddum Bounds for Total Domination | SpringerLink Skip to main content
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Let $ x_1,..., x_n $ be a list of real numbers, let $ s:=\sum_ {i= 1}^{n} x_i $, and let $
h:\mathbb {N}\rightarrow\mathbb {R} $ be a function. We gave a necessary and sufficient …

The study of graphical invariants on graph products has resulted in several famous
conjectures and open problems in graph theory. In this section, we investigate the behavior …

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 vertex $ u $ in a graph $ G $ totally dominates a vertex $ v $ if $ u $ is adjacent to $ v $ in $
G $. A total dominating set of $ G $ is a set $ S $ of vertices of $ G $ such that every vertex of …