@Article{CMR-33-4,
author = {Zhao, Yancai and Miao, Lianying},
title = {Signed Roman (Total) Domination Numbers of Complete Bipartite Graphs and Wheels},
journal = {Communications in Mathematical Research },
year = {2017},
volume = {33},
number = {4},
pages = {318--326},
abstract = {<p style="text-align: justify;">A signed (res. signed total) Roman dominating function, SRDF (res.
STRDF) for short, of a graph $G = (V, E)$ is a function $f : V$ → {$−1, 1, 2$} satisfying
the conditions that (i) $\sum\limits_{v∈N[v]}f(v) ≥ 1$ (res. $\sum\limits_{v∈N[v]}f(v) ≥ 1$) for any $v ∈ V$ , where $N[v]$ is the closed neighborhood and $N(v)$ is the neighborhood of $v$, and (ii) every
vertex $v$ for which $f(v) = −1$ is adjacent to a vertex $u$ for which $f(u) = 2$. The
weight of a SRDF (res. STRDF) is the sum of its function values over all vertices.
The signed (res. signed total) Roman domination number of $G$ is the minimum weight
among all signed (res. signed total) Roman dominating functions of $G$. In this paper,
we compute the exact values of the signed (res. signed total) Roman domination
numbers of complete bipartite graphs and wheels.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2017.04.04},
url = {https://global-sci.com/article/81627/signed-roman-total-domination-numbers-of-complete-bipartite-graphs-and-wheels}
}