Sandi Klavvzar

activity

20172026

most citedCharacterization of general position sets and its applications to cographs and bipartite graphs

3 citations · 8 across the 22 of their papers we have counts for

collaborators

25 papers

math.CO2026

Multiset resolvability parameters in graphs: A survey with new results and open problems

Mohammad Farhan, Sandi Klavžar, Dorota Kuziak +1

The metric dimension, which has lots of variants and numerous applications in other fields, is one of the most important and most extensively studied topics in metric graph theory.…

math.CO2026

Maker-Breaker Sabotage Game

Marko Jakovac, Sandi Klavžar, Mirjana Mikalački +1

The Maker-Breaker sabotage game is played on a graph $G$ by Runner and Blocker. They play in turns, Runner first moves along a not yet traversed edge from her current position, aft…

math.CO2026

Independent mutual-visibility sets and distance edge-critical graphs

Jing Tian, Csilla Bujtás, Sandi Klavžar

In this paper, connections between independent sets and the variety of mutual-visibility sets are studied. It is proved that every outer mutual-visibility set of a graph is indepen…

math.CO2025

Maker-Breaker resolving game played on lexicographic products of graphs

Savitha K S, Sandi Klavžar, Tijo James

In the Maker-Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph $G$ . The aim of Resolver is to select all the vert…

math.CO2025

Maker-Breaker total domination number

Athira Divakaran, Tijo James, Sandi Klavžar +1

The Maker-Breaker total domination number, $γ_{MBT} (G)$ , of a graph $G$ is introduced as the minimum number of moves of Dominator to win the Maker-Breaker total domination game…

math.CO2025

Intertwining local (adjacency) metric dimension with the clique number of a graph

Ali Ghalavand, Sandi Klavžar, Xueliang Li

Let $G$ be a simple connected graph with order $n (G)$ , local metric dimension $dim_{l} (G)$ , local adjacency metric dimension $dim_{A, l} (G)$ , and clique number $ω (G)$ ,…

math.CO2025

On Sierpiński packing chromatic number and recognition of Sierpiński products

Přemysl Holub, Sandi Klavžar

The Sierpiński product $G \otimes_{f} H$ of graphs $G$ and $H$ with respect to a function $f : V (G) \to V (H)$ has the vertex set $V (G) \times V (H)$ . For every $g \in V (G)$ …

math.CO2025

On the local metric dimension of $K_{4}$ -free graphs

Ali Ghalavand, Sandi Klavžar, Xueliang Li

Let $G$ be a graph of order $n (G)$ , local metric dimension $dim_{l} (G)$ , and clique number $ω (G)$ . It has been conjectured that if $n (G) \geq ω (G) + 1 \geq 4$ , then $ \dim_l…

math.CO2025

S-packing chromatic critical graphs

Gülnaz Boruzanlı Ekinci, Csilla Bujtás, Didem Gözüpek +1

For a non-decreasing sequence of positive integers $S = (s_{1}, s_{2}, \dots)$ , the $S$ -packing chromatic number of a graph $G$ is denoted by $χ_{S} (G)$ . In this paper, $χ_{S}$ -critical graph…

math.CO2024

On $ℓ$ -distance-balancedness of cubic Cayley graphs of dihedral groups

Gang Ma, Jianfeng Wang, Guang Li +1

A connected graph $Γ$ of diameter $diam (Γ) \geq ℓ$ is $ℓ$ -distance-balanced if $∣ W_{x y} (Γ) ∣ = ∣ W_{y x} (Γ) ∣$ for every $x, y \in V (Γ)$ with $d_{Γ} (x, y) = ℓ$ , where $W_{x y} (Γ)$ …

math.CO2024

Interplay between the local metric dimension and the clique number of a graph

Ali Ghalavand, Sandi Klavžar, Xueliang Li

The local metric dimension $dim_{l}$ in relation to the clique number $ω$ is investigated. It is proved that if $ω (G) \leq n (G) - 3$ , then $dim_{l} (G) \leq n (G) - 3$ and the gra…

math.CO2024

Breaking Symmetry in Graphs by Resolving Sets

Meysam Korivand, Nasrin Soltankhah, Sandi Klavžar

Let $dim (G)$ and $D (G)$ respectively denote the metric dimension and the distinguishing number of a graph $G$ . It is proved that $D (G) \leq dim (G) + 1$ holds for every con…

math.CO2024

Monophonic position sets of Cartesian and lexicographic products of graphs

Ullas Chandran S. V., Sandi Klavžar, Neethu P. K. +1

The general position problem in graph theory asks for the number of vertices in a largest set $S$ of vertices of a graph $G$ such that no shortest path of $G$ contains more than tw…

math.CO2023

Builder-Blocker General Position Games

Sandi Klavžar, Jing Tian, James Tuite

This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker,…

math.CO2023

Non- $ℓ$ -distance-balanced generalized Petersen graphs $GP (n, 3)$ and $GP (n, 4)$

Gang Ma, Jianfeng Wang, Sandi Klavžar

A connected graph $G$ of diameter $diam (G) \geq ℓ$ is $ℓ$ -distance-balanced if $∣ W_{x y} ∣ = ∣ W_{y x} ∣$ for every $x, y \in V (G)$ with $d_{G} (x, y) = ℓ$ , where $W_{x y}$ is the…

math.CO2022

Extremal results on stepwise transmission irregular graphs

Yaser Alizadeh, Sandi Klavžar

The transmission $Tr_{G} (v)$ of a vertex $v$ of a connected graph $G$ is the sum of distances between $v$ and all other vertices in $G$ . $G$ is a stepwise transmission irregula…

math.CO2021★ 1 cited

Zero forcing number versus general position number in tree-like graphs

Hongbo Hua, Xinying Hua, Sandi Klavžar

Let $Z (G)$ and $gp (G)$ be the zero forcing number and the general position number of a graph $G$ , respectively. Known results imply that $gp (T) \geq Z (T) + 1$ …

math.CO2021

The general position achievement game played on graphs

Sandi Klavžar, Neethu P. K., Ullas Chandran S.

A general position set of a graph $G$ is a set of vertices $S$ in $G$ such that no three vertices from $S$ lie on a common shortest path. In this paper we introduce and study the g…

math.CO2021

A characterization of 4- $χ_{S}$ -vertex-critical graphs for packing sequences with $s_{1} = 1$ and $s_{2} \geq 3$

Sandi Klavžar, Hui Lei, Xiaopan Lian +1

If $S = (s_{1}, s_{2}, \dots)$ is a non-decreasing sequence of positive integers, then the $S$ -packing $k$ -coloring of a graph $G$ is a mapping $c : V (G) \to [k]$ such that if $c(u)=…

math.CO2021★ 2 cited

Some binary products and integer linear programming for computing $k$ -metric dimension of graphs

Sandi Klavžar, Freydoon Rahbarnia, Mostafa Tavakoli

Let $G$ be a connected graph. For an ordered set $S = {v_{1}, \dots, v_{ℓ}} \subseteq V (G)$ , the vector $r_{G} (v ∣ S) = (d_{G} (v_{1}, v), \dots, d_{G} (v_{ℓ}, v))$ is called the metric $S$ -repr…

math.CO2020

Correcting the algorithm for the secure domination number of cographs by Jha, Pradhan, and Banerjee

Anja Kišek, Sandi Klavžar

Jha, Pradhan, and Banerjee devised a linear algorithm to compute the secure domination number of a cograph. Here it is shown that their Lemma~2, which is crucial for the computatio…

math.CO2020

On the general position number of complementary prisms

Neethu P. K., Ullas Chandran S. V., Manoj Changat +1

The general position number $gp (G)$ of a graph $G$ is the cardinality of a largest set of vertices $S$ such that no element of $S$ lies on a geodesic between two other elemen…

math.CO2018★ 3 cited

Characterization of general position sets and its applications to cographs and bipartite graphs

Bijo S. Anand, Ullas Chandran S. V., Manoj Changat +2

A vertex subset $S$ of a graph $G$ is a general position set of $G$ if no vertex of $S$ lies on a geodesic between two other vertices of $S$ . The cardinality of a largest general p…

math.CO2017★ 2 cited

Graph theory general position problem

Paul Manuel, Sandi Klavžar

The classical no-three-in-line problem is to find the maximum number of points that can be placed in the $n \times n$ grid so that no three points lie on a line. Given a set $S$ of…

Multiset resolvability parameters in graphs: A survey with new results and open problems

Maker-Breaker Sabotage Game

Independent mutual-visibility sets and distance edge-critical graphs

Maker-Breaker resolving game played on lexicographic products of graphs

Maker-Breaker total domination number

Intertwining local (adjacency) metric dimension with the clique number of a graph

On Sierpiński packing chromatic number and recognition of Sierpiński products

On the local metric dimension of K4​-free graphs

S-packing chromatic critical graphs

On ℓ-distance-balancedness of cubic Cayley graphs of dihedral groups

Interplay between the local metric dimension and the clique number of a graph

Breaking Symmetry in Graphs by Resolving Sets

Monophonic position sets of Cartesian and lexicographic products of graphs

Builder-Blocker General Position Games

Non-ℓ-distance-balanced generalized Petersen graphs GP(n,3) and GP(n,4)

Extremal results on stepwise transmission irregular graphs

Zero forcing number versus general position number in tree-like graphs

The general position achievement game played on graphs

A characterization of 4-χS​-vertex-critical graphs for packing sequences with s1​=1 and s2​≥3

Some binary products and integer linear programming for computing k-metric dimension of graphs

Correcting the algorithm for the secure domination number of cographs by Jha, Pradhan, and Banerjee

On the general position number of complementary prisms

Characterization of general position sets and its applications to cographs and bipartite graphs

Graph theory general position problem

On the local metric dimension of $K_{4}$ -free graphs

On $ℓ$ -distance-balancedness of cubic Cayley graphs of dihedral groups

Non- $ℓ$ -distance-balanced generalized Petersen graphs $GP (n, 3)$ and $GP (n, 4)$

A characterization of 4- $χ_{S}$ -vertex-critical graphs for packing sequences with $s_{1} = 1$ and $s_{2} \geq 3$

Some binary products and integer linear programming for computing $k$ -metric dimension of graphs