Iztok Peterin

activity

20172021

collaborators

10 papers

math.CO2021

Roman domination in direct product graphs and rooted product graphs

Abel Cabrera Martinez, Iztok Peterin, Ismael G. Yero

Let $G$ be a graph with vertex set $V (G)$ . A function $f : V (G) \to {0, 1, 2}$ is a Roman dominating function on $G$ if every vertex $v \in V (G)$ for which $f (v) = 0$ is adjacent…

math.CO2021

A Steiner general position problem in graph theory

Sandi Klavžar, Dorota Kuziak, Iztok Peterin +1

Let $G$ be a graph. The Steiner distance of $W \subseteq V (G)$ is the minimum size of a connected subgraph of $G$ containing $W$ . Such a subgraph is necessarily a tree called a Stei…

math.CO2020

Dominating the direct product of two graphs through total Roman strategies

Abel Cabrera Martinez, Dorota Kuziak, Iztok Peterin +1

Given a graph $G$ without isolated vertices, a total Roman dominating function for $G$ is a function $f : V (G) \to {0, 1, 2}$ such that every vertex with label 0 is adjacent…

math.CO2019

A note on bipartite graphs whose [1, k]-domination number equal to their number of vertices

Narges Ghareghani, Iztok Peterin, Pouyeh Sharifani

A subset $D$ of the vertex set $V$ of a graph $G$ is called an $[1, k]$ -dominating set if every vertex from $V - D$ is adjacent to at least one vertex and at most $k$ vertices of $D$ .…

math.CO2019

A note on the packing chromatic number of lexicographic products

Dragana Božović, Iztok Peterin

The packing chromatic number $χ_{ρ} (G)$ of a graph $G$ is the smallest integer $k$ such that there exists a $k$ -vertex coloring of $G$ in which any two vertices receiving color $i$ a…

math.CO2018

On three outer-independent domination related parameters in graphs

Doost Ali Mojdeh, Iztok Peterin, Babak Samadi +1

Let $G$ be a graph and let $S \subseteq V (G)$ . The set $S$ is a double outer-independent dominating set of $G$ if $∣ N [v] \cap D ∣ \geq 2$ , for all $v \in V (G)$ , and $V (G) ∖ S$ is…