Characterization of perfect Roman domination edge critical trees
Abstract
A perfect Roman dominating function on a graph $G =(V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$
satisfying the condition that every vertex $u$ with $f(u) = 0$ is adjacent to exactly one vertex
$v$ for which $f(v) = 2$. The weight of a perfect Roman dominating function $f$ is the sum of
the weights of the vertices. The perfect Roman domination number of $G$, denoted by $\gamma_{R}^{p}(G)$, is
the minimum weight of a perfect Roman dominating function in $G$. In this paper, we study the
graphs for which adding any new edge decreases the perfect Roman
domination number. We call these graphs $\gamma_R^p$-edge critical.
The purpose of this paper is to characterize the class of $\gamma_R^p$-edge critical trees.
Downloads
Published
Issue
Section
License
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
