S. Sheikholeslami

activity

20152024

most citedTotal Roman {2}-Dominating functions in Graphs

20 citations · 49 across the 10 of their papers we have counts for

collaborators

10 papers

math.CO2024★ 20 cited

Total Roman {2}-Dominating functions in Graphs

H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami +1

A Roman ${2}$ -dominating function (R2F) is a function $f : V \to {0, 1, 2}$ with the property that for every vertex $v \in V$ with $f (v) = 0$ there is a neighbor $u$ of $v$ wit…

math.CO2024★ 4 cited

On the outer independent total double Roman dominating functions

H. Abdolahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami +1

Let ${0, 1, \dots, t}$ be abbreviated by $[t] .$ A double Roman dominating function (DRDF) on a graph $Γ = (V, E)$ is a map $l : V \to [3]$ satisfying \textrm{(i)} if $l (r) = 0$ the…

math.CO2024★ 17 cited

Maximal double Roman domination in graphs

H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami +1

A maximal double Roman dominating function (MDRDF) on a graph $G = (V, E)$ is a function $f : V (G) \to {0, 1, 2, 3}$ such that \textrm{(i) }every vertex $v$ with $f (v) = 0$ is adjac…

math.CO2021

Roman domination in graphs with minimum degree at least two and some forbidden cycles

S. M. Sheikholeslami, M. Chellali, R. Khoeilar +2

Let $G = (V, E)$ be a graph of order $n$ and let $γ_{R} (G)$ and $\partial (G)$ denote the Roman domination number and the differential of $G,$ respectively. In this paper we prove tha…

math.CO2021★ 5 cited

Restrained condition on double Roman dominating functions

Babak Samadi, Nasrin Soltankhah, H. Abdollahzadeh Ahangar +4

We continue the study of restrained double Roman domination in graphs. For a graph $G=\big{(}V(G),E(G)\big{)}$, a double Roman dominating function $f$ is called a restrained double…

math.CO2021

New upper bounds for the forgotten index among bicyclic graphs

A. Jahanbani, L. Shahbazi, S. M. Sheikholeslami +2

The forgotten topological index of a graph $G$ , denoted by $F (G)$ , is defined as the sum of weights $d (u)^{2} + d (v)^{2}$ over all edges $uv$ of $G$ , where $d (u)$ denotes the degree…

math.CO2020

The Roman (k,k)-domatic number of a graph

A. P. Kazemi, S. M. Sheikholeslami, L. Volkmann

Let $k$ be a positive integer. A {\em Roman $k$ -dominating function} on a graph $G$ is a labeling $f : V (G) ⟶ {0, 1, 2}$ such that every vertex with label 0 has at le…

math.CO2019

On the total and strong version for Roman dominating functions in graphs

S. Nazari-Moghaddam, M. Soroudi, S. M. Sheikholeslami +1

Consider a finite and simple graph $G = (V, E)$ with maximum degree $Δ$ . A strong Roman dominating function over the graph $G$ is understood as a map $f : V (G)\rightarrow \{0, 1,\ldo…

math.CO2018

Changing and unchanging 2-rainbow independent domination

Pu Wu, Zehui Shao, Vladimir Samodivkin +3

For a function $f : V (G) \to {0, 1, 2}$ we denote by $V_{i}$ the set of vertices to which the value $i$ is assigned by $f$ , i.e. $V_{i} = {x \in V (G) : f (x) = i}$ . If…

math.CO2015★ 3 cited

On the Strong Roman Domination Number of Graphs

M. P. Alvarez-Ruiz, I. Gonzalez Yero, T. Mediavilla-Gradolph +2

Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having t…