Total Domination Value in Graphs
Year: 2012
Type: article
Abstract: A set $D \subseteq V(G)$ is a \emph{total dominating set} of $G$ if for every vertex $v \in V(G)$ there exists a vertex $u \in D$ such that $u$ and $v$ are adjacent. A total dominating set of $G$ of minimum cardinality is called a $γ_t(G)$-set. For each vertex $v \in V(G)$, we define the \emph{total domination value} of $v$, $TDV(v)$, to be the number of $γ_t(G)$-sets to which $v$belongs. This definition gives rise to \emph{a local study of total domination} in graphs. In this paper, we study some basic properties of the $TDV$ function; also, we derive explicit formulas for the $TDV$ of any complete n-partite graph, any cycle, and any path.
Source: Utilitas Mathematica
Author: Kang, Cong X.
Institutions: Texas A&M University at Galveston, Texas A&M University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1600305589