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THE MINIMUM ECCENTRIC-DOMINATING ENERGY OF A GRAPH
Keywords:
minimum eccentric-dominating set, minimum eccentric-dominating matrix, minimum eccentric-dominating eigenvaluesDOI:
https://doi.org/10.17654/0972087124020Abstract
Let $G$ be a simple graph. A subset $S$ of vertices in $G$ is said to be an eccentric-dominating set if for each vertex not in $S$, there exists at least one eccentric vertex in $S$ and $N[S]=G$. The cardinality of the minimum eccentric-dominating set is called the eccentric domination number, denoted by $\gamma_{e d}(G)$. In this article, we define and study the minimum eccentric-dominating energy $E_{e d}(G)$, and compute the exact value for some standard classes of graphs. Also, we establish some bounds for $E_{e d}(G)$.
Received: July 4, 2024
Revised: August 25, 2024
Accepted: September 28, 2024
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