February 9, 2023

# Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

## Research

 Title On the Outer Independent Double Roman Domination Number Type Article Keywords (Outer independent) double Roman domination number, Roman domination number, Vertex cover number Journal Bulletin of the Iranian Mathematical Society DOI https://doi.org/10.1007/s41980-021-00606-7 Researchers a { color: #4f98b0; } a:hover { color: #ffab00; } a:link:visited { text-decoration: none; } Doost Ali Mojdeh (First researcher) , Babak Samadi (Second researcher) , Zehui Shao (Third researcher) , Ismael Gonzalez Yero (Fourth researcher)

## Abstract

An outer independent (double) Roman dominating function is a (double) Roman dominating function $f$ for which the set of vertices assigned $0$ under $f$ is independent. The outer independent (double) Roman domination number ($\gamma_{oidR}(G)$) $\gamma_{oiR}(G)$ is the minimum weight taken over all outer independent (double) Roman dominating functions of $G$. A vertex cover number $\beta(G)$ is the minimum size of any vertex cover sets of a graph $G$. In this work, we present some contributions to the study of outer independent double Roman domination in graphs. Characterizations of the families of all connected graphs with small outer independent double Roman domination numbers, and tight lower and upper bounds on this parameter are given. We also prove that the decision problem associated with $\gamma_{oidR}(G)$ is NP-complete even when restricted to planar graphs with maximum degree at most four. We moreover prove that $2\beta(T)+1\leq \gamma_{oidR}(T)\leq 3\beta(T)$ for any tree $T$, and show that each integer between the lower and upper bounds is realizable. Finally, we give an exact formula for this parameter concerning the corona graphs.