Iztok Peterin

activity

20122026

most citedDistance magic labeling and two products of graphs

20 citations · 67 across the 25 of their papers we have counts for

collaborators

Showing math.COShow all

33 papers · 1 filter

math.CO2026

On the Independence Number of the Modular Product

Tanja Dravec, Iztok Peterin

The \emph{modular product} $G ⋄ H$ of graphs $G$ and $H$ is a graph on vertex set $V (G) \times V (H)$ . Two vertices $(g, h)$ and $(g^{'}, h^{'})$ of $G ⋄ H$ are adjacent if $g=g'…

math.CO2026

On externally supported independence number of graphs

Dragana Božović, Iztok Peterin, Adriana Roux +1

We introduce the \emph{externally supported independence number} $α_{es} (G)$ of a graph $G$ as the maximum cardinality of an independent set $B$ with an additional condition, t…

math.CO2025

On acyclic b-chromatic number of cubic graphs

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G$ be a graph. An acyclic $k$ -coloring of $G$ is a map $c : V (G) \to {1, \dots, k}$ such that $c (u) \neq = c (v)$ for any $uv \in E (G)$ and the subgraph induced by the vertice…

math.CO2025

Independent mutual-visibility coloring and related concepts

Boštjan Brešar, Iztok Peterin, Babak Samadi +1

Given a graph $G$ , a subset $M \subseteq V (G)$ is a mutual-visibility (MV) set if for every $u, v \in M$ , there exists a $u, v$ -geodesic whose internal vertices are not in $M$ . We inve…

math.CO2025

On the star b-chromatic number of a graph

Dragana Božović, Daša Mesarič Štesl, Iztok Peterin

A star coloring of a graph $G$ is a proper coloring where vertices of every two color classes induce a forest of stars. A strict partial order is defined on the set of all star col…

math.CO2025

On the stress transit function

Arun Anil, Manoj Changat, Tanja Dravec +5

The stress interval $S (u, v)$ between $u, v \in V (G)$ is the set of all vertices in a graph $G$ that lie on every shortest $u, v$ -path. A set $U \subseteq V (G)$ is stress convex if $S(…

math.CO2024

Grundy Packing Coloring of Graphs

Didem Gözüpek, Iztok Peterin

A map $c : V (G) \to {1, \dots, k}$ of a graph $G$ is a packing $k$ -coloring if every two different vertices of the same color $i \in {1, \dots, k}$ are at distance more than $i$ …

math.CO2024★ 1 cited

Convex Geometries yielded by Transit Functions

Manoj Changat, Lekshmi Kamal K. Sheela, Iztok Peterin +1

Let $V$ be a finite nonempty set. A transit function is a map $R : V \times V \to 2^{V}$ such that $R (u, u) = {u}$ , $R (u, v) = R (v, u)$ and $u \in R (u, v)$ hold for every $u, v \in V$ . A…

math.CO2024

Domination number of modular product graphs

Sergio Bermudo, Iztok Peterin, Jelena Sedlar +1

The modular product $G ⋄ H$ of graphs $G$ and $H$ is a graph on vertex set $V (G) \times V (H)$ . Two vertices $(g, h)$ and $(g^{'}, h^{'})$ of $G ⋄ H$ are adjacent…

math.CO2024★ 1 cited

On Distance and Strong Metric Dimension of the Modular Product

Cong X. Kang, Aleksander Kelenc, Iztok Peterin +1

The modular product $G ⋄ H$ of graphs $G$ and $H$ is a graph on vertex set $V (G) \times V (H)$ . Two vertices $(g, h)$ and $(g^{'}, h^{'})$ of $G ⋄ H$ are adjacent if $g = g^{'}$ and $…

math.CO2023

A new approach to b-coloring of regular graphs

Magda Dettlaff, Hanna Furmańczyk, Iztok Peterin +2

Let $G$ be a graph and c a proper k-coloring of G, i.e. any two adjacent vertices u and v have different colors c(u) and c(v). A proper k-coloring is a b-coloring if there exists a…

math.CO2023★ 1 cited

The Toll Walk Transit Function of a Graph: Axiomatic Characterizations and First-Order Non-definability

Manoj Changat, Jeny Jacob, Lekshmi Kamal K. Sheela +1

A walk $W = w_{1} w_{2} \dots w_{k}$ , $k \geq 2$ , is called a toll walk if $w_{1} \neq = w_{k}$ and $w_{2}$ and $w_{k - 1}$ are the only neighbors of $w_{1}$ and $w_{k}$ , respectively, on $W$ in a graph $G$ …

math.CO2023

Resolving vertices of graphs with differences

Iztok Peterina, Jelena Sedlar, Riste Škrekovski +1

The classical (vertex) metric dimension of a graph G is defined as the cardinality of a smallest set S in V (G) such that any two vertices x and y from G have different distances t…

math.CO2022★ 4 cited

On b-acyclic chromatic number of a graph

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G$ be a graph. We introduce the acyclic b-chromatic number of $G$ as an analogue to the b-chromatic number of $G$ . An acyclic coloring of a graph $G$ is a map $c:V(G)\rightarr…

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.CO2021

The Simultaneous Fractional Dimension of Graph Families

Cong X. Kang, Iztok Peterin, Eunjeong Yi

A subset $S$ of the vertices $V$ of a connected graph $G$ resolves $G$ if no two vertices of $V$ share the same list of distances (shortest-path metric) with respect to the vertice…

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.CO2019★ 1 cited

(Open) packing number of some graph products

Doost Ali Mojdeh, Iztok Peterin, Babak Samadi +1

The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is t…

math.CO2018★ 16 cited

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…

math.CO2018

Incidence dimension and 2-packing number in graphs

Dragana Bozovic, Aleksander Kelenc, Iztok Peterin +1

Let $G = (V, E)$ be a graph. A set of vertices $A$ is an incidence generator for $G$ if for any two distinct edges $e, f \in E (G)$ there exists a vertex from $A$ which is an endpoint of…

math.CO2018

Edge metric dimension of some graph operations

Iztok Peterin, Ismael G. Yero

Let $G = (V, E)$ be a connected graph. Given a vertex $v \in V$ and an edge $e = u w \in E$ , the distance between $v$ and $e$ is defined as $d_{G} (e, v) = min {d_{G} (u, v), d_{G} (w, v)}$ . A nonempt…