Ever since the discovery of domination numbers by Claude Berge in the year 1958, graph
domination has become an important domain in graph theory that has strengthened itself as …

The independence number of a graph is the maximum number of vertices from the vertex set
of the graph such that no two vertices are adjacent. We systematically examine a collection …

We discuss a new implementation of, and new experiments with, Fajtlowicz's Dalmatian
conjecture-making heuristic. Our program makes conjectures about relations of real number …

For a sequence d of nonnegative integers, let and be the sets of all graphs and forests with
degree sequence d, respectively. Let,,, and where is the domination number and is the …

Suppose G=(V,E) is a graph with no isolated vertex. A subset S of V is called a locating-total
dominating set of G if every vertex in V is adjacent to a vertex in S, and for every pair of …

Let $ G $ be a simple graph with vertex set $ V (G) $. A set $ S\subseteq V (G) $ is
independent if no two vertices from $ S $ are adjacent. For $ X\subseteq V (G) $, the …

A set S of vertices in a graph G is a 2-dominating set if every vertex of G not in S is adjacent
to at least two vertices in S. The 2-domination number γ 2 (G) is the minimum cardinality of a …

In this paper we study relationships between the\emph {matching number}, written $\mu (G)
$, and the\emph {independence number}, written $\alpha (G) $. Our first main result is to …

Let G be a simple graph with vertex set V G. A set A⊆ VG is independent if no two vertices
from A are adjacent. If α G+ μ G=| VG|, then G is called a König–Egerváry graph (Deming …

Abstract The 2-domination number γ 2 (G) of a graph G is the order of a smallest set D⊆ V
(G) such that each vertex of V (G)∖ D is adjacent to at least two vertices in D. The …