Sandi Klavžar

activity

20192026

most citedMetric dimensions of generalized Sierpiński graphs over squares

4 citations · 14 across the 17 of their papers we have counts for

collaborators

19 papers

math.CO2026

Improved Lower Bounds on the General Reduced Second Zagreb Index of Trees and Unicyclic Graphs

Nasrin Dehgardi, Sandi Klavžar, Mahdieh Azari

For a simple graph $Γ$ and a real number $λ$ , the general reduced second Zagreb index is defined by the formula $GR M_{λ} (Γ) = ab \in E (Γ) \sum [(°_{Γ} (a) + λ) (°_{Γ} (b) + λ)] .$ A sharp lowe…

math.CO2026

Wiener and Average Distance of Irregular Square-Cell Configuration

S. Prabhu, Sandi Klavžar, M. Anitha +2

A subgraph of the square lattice with all of its inner faces being 4-cycles is called a square-cell configuration. Prior work has provided explicit expressions for the total and av…

math.CO2025

On $d$ -distance $p$ -packing domination number in strong products

Csilla Bujtás, Vesna Iršič Chenoweth, Sandi Klavžar +1

The $d$ -distance $p$ -packing domination number $γ_{d}^{p} (G)$ of a graph $G$ is the cardinality of a smallest set of vertices of $G$ which is both a $d$ -distance dominating set and a $…

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

Moving through Cartesian products, coronas and joins in general position

Sandi Klavžar, Aditi Krishnakumar, Dorota Kuziak +3

The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was de…

math.CO2025

Varieties of mutual-visibility and general position on Sierpiński graphs

Dhanya Roy, Sandi Klavžar, Aparna Lakshmanan +1

The variety of mutual-visibility problems contains four members, as does the variety of general position problems. The basic problem is to determine the cardinality of the largest…

math.CO2025★ 1 cited

Three algorithmic approaches to the general position problem

Zahra Hamed-Labbafian, Narjes Sabeghi, Mostafa Tavakoli +1

If $G$ is a graph, then $X \subseteq V (G)$ is a general position set if for every two vertices $v, u \in X$ and every shortest $(u, v)$ -path $P$ , it holds that no inner vertex of $P$ l…

math.CO2025

Criticality for Maker-Breaker domination games with predomination

Csilla Bujtás, Pakanun Dokyeesun, Sandi Klavžar +1

A predominated graph is a pair $(G, D)$ , where $G$ is a graph and the vertices in $D \subseteq V (G)$ are considered already dominated. Maker-Breaker domination game critical (MBD cri…

math.CO2025

The General Position Problem: A Survey

Ullas Chandran S. V., Sandi Klavžar, James Tuite

Inspired by a chessboard puzzle of Dudeney, the general position problem in graph theory asks for a largest set $S$ of vertices in a graph such that no three elements of $S$ lie on…

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

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★ 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★ 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

Variety of general position problems in graphs

Jing Tian, Sandi Klavžar

Let $X$ be a vertex subset of a graph $G$ . Then $u, v \in V (G)$ are $X$ -positionable if $V (P) \cap X \subseteq {u, v}$ holds for any shortest $u, v$ -path $P$ . If each two vertices fr…

math.CO2023

Extremal edge general position sets in some graphs

Jing Tian, Sandi Klavžar, Elif Tan

A set of edges $X \subseteq E (G)$ of a graph $G$ is an edge general position set if no three edges from $X$ lie on a common shortest path. The edge general position number ${\rm gp}…

math.CO2019

A Lower Bound and Several Exact Results on the $d$ -Lucky Number

Sandi Klavžar, Indra Rajasingh, D. Ahima Emilet

If $ℓ : V (G) \to N$ is a vertex labeling of a graph $G = (V (G), E (G))$ , then the $d$ -lucky sum of a vertex $u \in V (G)$ is $d_\ell(u) = d_G(u) + \sum_{v\in N(u)}\…

Improved Lower Bounds on the General Reduced Second Zagreb Index of Trees and Unicyclic Graphs

Wiener and Average Distance of Irregular Square-Cell Configuration

On d-distance p-packing domination number in strong products

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

Moving through Cartesian products, coronas and joins in general position

Varieties of mutual-visibility and general position on Sierpiński graphs

Three algorithmic approaches to the general position problem

Criticality for Maker-Breaker domination games with predomination

The General Position Problem: A Survey

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

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

General position problems in strong and lexicographic 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

Variety of general position problems in graphs

Extremal edge general position sets in some graphs

A Lower Bound and Several Exact Results on the d-Lucky Number

On $d$ -distance $p$ -packing domination number in strong products

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

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

A Lower Bound and Several Exact Results on the $d$ -Lucky Number