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Locating Domination in Bipartite Graphs and Their Complements by Hernando, Carmen; Mora, Mercè; Pelayo, Ignacio M. is a scholarly article available to read on EtoBox.

What is Locating Domination in Bipartite Graphs and Their Complements about?

A set $S$ of vertices of a graph $G$ is \emph{distinguishing} if the sets of neighbors in $S$ for every pair of vertices not in $S$ are distinct. A \emph{locating-dominating set} of $G$ is a dominating distinguishing set. The \emph{location-domination number} of $G$, $\lambda(G)$, is the minimum cardinality of a locating-dominating set. In this work we study relationships between $\lambda({G})$ and $\lambda (\overline{G})$ for bipartite graphs. The main result is the characterization of all connected bipartite graphs $G$ satisfying $\lambda (\overline{G})=\lambda({G})+1$. To this aim, we define an edge-labeled graph $G^S$ associated with a distinguishing set $S$ that turns out to be very helpful.

Author

Hernando, Carmen; Mora, Mercè; Pelayo, Ignacio M.

Published

2017

Language

EN