Kaustav Paul

activity

20242026

collaborators

6 papers

math.CO2026

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

Juan GutiÃ©rrez, Kaustav Paul

Given a graph $G$ , the domination number $I^^{3} (G)$ is the minimum cardinality of a dominating set in $G$ , and the packing number $I ¨ (G)$ is the maximum cardinality of a set of vertic…

math.CO2026

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…

cs.CC2024

(Independent) Roman Domination Parameterized by Distance to Cluster

Pradeesha Ashok, Gautam K. Das, Arti Pandey +2

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

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…

cs.DM2024

Algorithmic Results for Weak Roman Domination Problem in Graphs

Kaustav Paul, Ankit Sharma, Arti Pandey

Consider a graph $G = (V, E)$ and a function $f : V \to {0, 1, 2}$ . A vertex $u$ with $f (u) = 0$ is defined as \emph{undefended} by $f$ if it lacks adjacency to any vertex w…