Kaustav Paul

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20242026

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4 papers · 1 filter

math.CO2026

Improved Domination--Packing Bounds in Claw-Free Cubic Graphs and Unit Disk Graphs

Juan Gutiérrez, Kaustav Paul

Given a graph $G$ , the domination number $γ (G)$ is the minimum cardinality of a dominating set in $G$ , and the packing number $ρ (G)$ is the maximum cardinality of a set of vertices…

math.CO2025

Locating-dominating partitions for some classes of graphs

Florent Foucaud, Paras Vinubhai Maniya, Kaustav Paul +1

A dominating set of a graph $G$ is a set $D \subseteq V (G)$ such that every vertex in $V (G) ∖ D$ is adjacent to at least one vertex in $D$ . A set $L \subseteq V (G)$ is a loc…

math.CO2025

Characterizing optimal monitoring edge-geodetic sets for some structured graph classes

Florent Foucaud, Arti Pandey, Kaustav Paul

Given a graph $G = (V, E)$ , a set $S \subseteq V$ is said to be a monitoring edge-geodetic set if the deletion of any edge in the graph results in a change in the distance between at l…

math.CO2024

Exploring Algorithmic Solutions for the Independent Roman Domination Problem in Graphs

Kaustav Paul, Ankit Sharma, Arti Pandey

Given a graph $G = (V, E)$ , a function $f : V \to {0, 1, 2}$ is said to be a \emph{Roman Dominating function} if for every $v \in V$ with $f (v) = 0$ , there exists a vertex $u \in N (v)$ such…