University of Ljubljana

output

19932026

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing math.COShow all

146 papers · 1 filter

math.CO2025★ 1 cited

Revisiting $d$ -distance (independent) domination in trees and in bipartite graphs

Csilla Bujtás, Vesna Iršič Chenoweth, Sandi Klavžar +1

The $d$ -distance $p$ -packing domination number $γ_{d}^{p} (G)$ of $G$ is the minimum size of a set of vertices of $G$ which is both a $d$ -distance dominating set and a $p$ -packing. In 1…

math.CO2025

Self-reverse labelings of distance magic graphs

Petr Kovář, Ksenija Rozman, Primož Šparl

A graph is distance magic if it admits a bijective labeling of its vertices by integers from $1$ up to the order of the graph in such a way that the sum of the labels of all the ne…

math.CO2025

Bounds on the game isolation number and exact values for paths and cycles

Csilla Bujtás, Tanja Dravec, Michael A. Henning +1

The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected onl…

math.CO2025

Orthogonalisability of joins of graphs

Rupert H. Levene, Polona Oblak, Helena Šmigoc

A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some…

math.CO2025

Thresholds for the biased Maker-Breaker domination games

Boštjan Brešar, Csilla Bujtás, Pakanun Dokyeesun +1

In the $(a, b)$ -biased Maker-Breaker domination game, two players alternately select unplayed vertices in a graph $G$ such that Dominator selects $a$ and Staller selects $b$ vertice…

math.CO2025

Enumerating the number of $k$ -matchings in successively amalgamated graphs

Simon Grad, Sandi Klavžar

In this paper, the transfer matrix technique using the $k$ -matching vector is developed to compute the number of $k$ -matchings in an arbitrary graph which can be constructed by suc…

math.CO2025

On decycling and forest numbers of Cartesian products of trees

Ali Ghalavand, Sandi Klavžar, Ning Yang

The decycling number $\nabla (G)$ of a graph $G$ is the minimum number of vertices that must be removed to eliminate all cycles in $G$ . The forest number $f (G)$ is the maximum numbe…

math.CO2024★ 1 cited

Visibility polynomials, dual visibility spectrum, and characterization of total mutual-visibility sets

Csilla Bujtás, Sandi Klavžar, Jing Tian

Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the…

math.CO2024★ 1 cited

Extremal results on $k$ -stepwise irregular graphs

Yaser Alizadeh, Sandi Klavžar, Javaher Langari

For a positive integer $k \geq 1$ , a graph $G$ is $k$ -stepwise irregular ( $k$ -SI graph) if the degrees of every pair of adjacent vertices differ by exactly $k$ . Such graphs are neces…

math.CO2024

Counting largest mutual-visibility and general position sets of glued $t$ -ary trees

Dhanya Roy, Sandi Klavžar, Aparna Lakshmanan S

All four invariants of the mutual-visibility problem and, all four invariants of the general position problem are determined for glued binary trees. The number of the corresponding…

math.CO2024

On the fractional matching extendability of Cayley graphs of Abelian groups

Boštjan Kuzman, Primož Šparl

Fractional matching extendability is a concept that brings together two widely studied topics in graph theory, namely that of fractional matchings and that of matching extendabilit…

math.CO2024★ 1 cited

General position problems in strong and lexicographic products of graphs

Pakanun Dokyeesun, Sandi Klavžar, Dorota Kuziak +1

Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general…

math.CO2024

Maker-Breaker domination game critical graphs

Athira Divakaran, Tanja Dravec, Tijo James +2

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$ . The goal of Domi…

math.CO2024★ 1 cited

On ${1, 2}$ -distance-balancedness of generalized Petersen graphs

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.CO2024★ 1 cited

Maker-Breaker resolving game played on corona products of graphs

Tijo James, Sandi Klavžar, Dorota Kuziak +2

The Maker-Breaker resolving game is a game played on a graph $G$ by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex…

math.CO2024★ 1 cited

The general position number under vertex and edge removal

Pakanun Dokyeesun, Sandi Klavžar, Jing Tian

Let $gp (G)$ be the general position number of a graph $G$ . It is proved that $gp (G - x) \leq 2 gp (G)$ holds for any vertex $x$ of a connected graph $G$ and that if $x…

math.CO2024★ 2 cited

General position sets, colinear sets, and Sierpiński product graphs

Sandi Klavžar, Jing Tian

Let $G \otimes_{f} H$ denote the Sierpiński product of graphs $G$ and $H$ with respect to the function $f$ . The Sierpiński general position number $gp_{S} (G, H)$ is intro…

math.CO2024★ 4 cited

Metric dimensions of generalized Sierpiński graphs over squares

Savari Prabhu, T. Jenifer Janany, Sandi Klavžar

Metric dimension is a valuable parameter that helps address problems related to network design, localization, and information retrieval by identifying the minimum number of landmar…

math.CO2024★ 3 cited

Mutual-visibility and general position in double graphs and in Mycielskians

Dhanya Roy, Sandi Klavžar, Aparna Lakshmanan

The general position problem in graphs is to find the maximum number of vertices that can be selected such that no three vertices lie on a common shortest path. The mutual-visibili…

math.CO2024

On the $Δ$ -edge stability number of graphs

Saieed Akbari, Reza Hosseini Dolatabadi, Mohsen Jamaali +2

The $Δ$ -edge stability number $es_{Δ} (G)$ of a graph $G$ is the minimum number of edges of $G$ whose removal results in a subgraph $H$ with $Δ (H) = Δ (G) - 1$ . Sets whose removal…

math.CO2024★ 1 cited

Maker-Breaker domination game played on corona products of graphs

Athira Divakaran, Tijo James, Sandi Klavžar +1

In the Maker-Breaker domination game, Dominator and Staller play on a graph $G$ by taking turns in which each player selects a not yet played vertex of $G$ . Dominator's goal is to…

math.CO2023★ 5 cited

Classification of cubic tricirculant nut graphs

Ivan Damnjanović, Nino Bašić, Tomaž Pisanski +1

A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that the…

math.CO2023★ 1 cited

Vertex-primitive digraphs with large fixity

Marco Barbieri, Primož Potočnik

The relative fixity of a digraph $Γ$ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of $Γ$ and the number of vertices of $Γ$ . We…

math.CO2023★ 2 cited

Symmetric Nonnegative Trifactorization of Pattern Matrices

Damjana Kokol Bukovšek, Helena Šmigoc

A factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $B C B^{T}$ , where $C$ is a $k \times k$ symmetric matrix, and both $B$ and $C$ are required to be nonne…

Revisiting d-distance (independent) domination in trees and in bipartite graphs

Self-reverse labelings of distance magic graphs

Bounds on the game isolation number and exact values for paths and cycles

Orthogonalisability of joins of graphs

Thresholds for the biased Maker-Breaker domination games

Enumerating the number of k-matchings in successively amalgamated graphs

On decycling and forest numbers of Cartesian products of trees

Visibility polynomials, dual visibility spectrum, and characterization of total mutual-visibility sets

Extremal results on k-stepwise irregular graphs

Counting largest mutual-visibility and general position sets of glued t-ary trees

On the fractional matching extendability of Cayley graphs of Abelian groups

General position problems in strong and lexicographic products of graphs

Maker-Breaker domination game critical graphs

On {1,2}-distance-balancedness of generalized Petersen graphs

Maker-Breaker resolving game played on corona products of graphs

The general position number under vertex and edge removal

General position sets, colinear sets, and Sierpiński product graphs

Metric dimensions of generalized Sierpiński graphs over squares

Mutual-visibility and general position in double graphs and in Mycielskians

On the Δ-edge stability number of graphs

Maker-Breaker domination game played on corona products of graphs

Classification of cubic tricirculant nut graphs

Vertex-primitive digraphs with large fixity

Symmetric Nonnegative Trifactorization of Pattern Matrices

Revisiting $d$ -distance (independent) domination in trees and in bipartite graphs

Enumerating the number of $k$ -matchings in successively amalgamated graphs

Extremal results on $k$ -stepwise irregular graphs

Counting largest mutual-visibility and general position sets of glued $t$ -ary trees

On ${1, 2}$ -distance-balancedness of generalized Petersen graphs

On the $Δ$ -edge stability number of graphs