TL;DR
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.
Let G be a graph with vertex-set and edge-set V(G) and E(G), respectively. Then S \subseteq V(G) is a hop independent J-dominating if S is both a hop independent and J-dominating set of G. The maximum cardinality of a hop independent J-dominating set of G, denoted by \gamma^{hi}_{J}(G) is the hop independent J-dominati...
Let G be a nontrivial graph. A set D ⊆ V(G) is a double dominating set of G if | \mathrm{N_G} [v] ∩ D| ≥ 2 for every vertex v ∈ V(G), where \mathrm{N_G} [v] represents the closed neighborhood of v. The double domination number of G is the minimum cardinality among all double dominating sets of G. In this paper we...
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...
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...
An independent dominating set I of a graph G is an independent set such that every vertex in V(G)−I has at least one neighbor in I. The independent domination number of G is the minimum cardinality of an independent dominating set of G. The independent bondage number of a graph G, denoted by bi(G), is the minimum cardi...
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...
We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.
