Independent Equitable Domination in Graphs Quiz

The neighborhood of a vertex v in a graph G, denoted as $N_G(v)$, is the set of all vertices adjacent to v, i.e., $N_G(v) = {u \in V(G) : uv \in E(G)}$.

The open neighborhood of a set D in a graph G, denoted as $N_G(D)$, is the set of all vertices adjacent to any vertex in D, i.e., $N_G(D) = \bigcup_{v \in D} N_G(v)$. The closed neighborhood of a set D in a graph G, denoted as $N_G[D]$, is the set of D and all vertices adjacent to any vertex in D, i.e., $N_G[D] = D \cup N_G(D)$.

In the context of a graph G, ∆(G) represents the maximum degree of G, given by $\max_{v \in V} \text{deg}(v)$, and δ(G) represents the minimum degree of G, given by $\min_{v \in V} \text{deg}(v)$.

<p>The focus of this paper's study is on the independent equitable domination of graphs, determining the independent equitable domination number of some graphs, and investigating graphs with the existence of independent equitable dominating set.</p> Signup and view all the answers

<p>One of the interesting facts about the study of connectivity and working in the area of domination in Graph Theory is the popularity of the concept of domination and its applications.</p> Signup and view all the answers