Vertex-Addition Strategy for Domination-Like Invariants

Vertex-Addition Strategy for Domination-Like Invariants

In [J. Graph Theory 13 (1989) 749–762], McCuaig and Shepherd gave an upper bound of the domination number for connected graphs with minimum degree at least two. In this paper, we propose a simple strategy which, together with the McCuaig-Shepherd theorem, gives a sharp upper bound of the domination number via the number of leaves. We also apply the same strategy to other domination-like invaria...

Splice Graphs and their Vertex-Degree-Based Invariants

Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

Majority domination vertex critical graphs

This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex fromG can change the majority domination number is surveyed for trees. Characterisation of V + M (G) and V − M (G) are determined.

On Domination of a Vertex as Exponentially

The assessment of the stability and the vulnerability of complex networks is the important concept while studying of them. In the literature, a sort of measures have been given in order to assessment the stability of systems. And also, some graph-theoretic parameters have been formed to provide formulas which calculate the reliability of a network. In this paper, we study the vulnerability of s...

Vertex Domination Critical in Circulant Graphs