2-Distance Certified Independence in the Join of Two Graphs

2-Distance Certified Independence in the Join of Two Graphs.

Given a simple and undirected graph G=(V(G),E(G)). Then R\subseteq V(G) is called a 2-distance certified independent set of G if R satisfies the following two conditions:(i)For every x\in R, x has either zero or at least two hop neighborhood in V(G)\setminus R; and (ii) R is an independent set of G. The 2-distance cer...

On 3-Distance Independent Sets of Graphs.

Let G be a graph with vertex set V(G) and edge set E(G). A set S \subseteq V(G) is a 3-distance independent set of G if d_G(v,w) \neq 3 for any two distinct vertices v,w \in S. The maximum cardinality of a 3-distance independent set of G, denoted by \alpha^3(G), is called the 3-distance independence number of G. In thi...

Independence number, essential connectivity and the distance spectral radius of graphs

An independent set of a graph G is a subset of VG, no two of which are adjacent. The cardinality of a maximum independent set in a graph G is called the independence number of G, denoted by alpha(G). The essential connectivity kappa'(G) of a graph G is denoted as the minimum number of vertices of G whose removal produc...

(In)tractability of the maximum 2 -clique problem for bipartite graphs

Independent domination in central graphs

Let $G$ be a graph with vertex set $V(G)$. A set $I\subseteq V(G)$ is an independent dominating set of $G$ if no two vertices in $I$ are adjacent and every vertex in $V(G)\setminus I$ is adjacent to at least one vertex in $I$. The independent domination number of $G$ is the minimum cardinality among all independent dom...

Theory & Applications of Graphs Theory & Applications of Graphs

This work establishes general properties of k -total bondage and finds exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.