Sk Samim Islam

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20232026

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5 papers · 1 filter

cs.DM2026

On the Complexity of Hop Domination and 2-Step Domination in Graph Classes

Sandip Das, Sweta Das, Sk Samim Islam

The domination problem is a well-studied problem in graph theory. In this paper, we study two natural variants: the hop domination problem and the $2$ -step domination problem. Let…

cs.DM2026

Multipacking on graphs and Euclidean metric space

Sk Samim Islam

A \emph{multipacking} in an undirected graph $G = (V, E)$ is a set $M \subseteq V$ such that for every vertex $v \in V$ and for every integer $r \geq 1$ , the ball of radius $r$ around…

cs.DM2024

Growth Rate of the Number of Empty Triangles in the Plane

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +1

Given a set $P$ of $n$ points in the plane, in general position, denote by $N_{Δ} (P)$ the number of empty triangles with vertices in $P$ . In this paper we investigate by how much $N_…

cs.DM2023

Relation between broadcast domination and multipacking numbers on chordal and other hyperbolic graphs

Sandip Das, Florent Foucaud, Sk Samim Islam +1

For a graph $G = (V, E)$ with a vertex set $V$ and an edge set $E$ , a function $f : V \to {0, 1, 2, ..., d iam (G)}$ is called a \emph{broadcast} on $G$ . For e…

cs.DM2023

Multipacking and broadcast domination on cactus graph and its impact on hyperbolic graph

Sandip Das, Sk Samim Islam

For a graph $G$ , $m p (G)$ is the multipacking number, and $γ_{b} (G)$ is the broadcast domination number. It is known that $m p (G) \leq γ_{b} (G)$ and $γ_{b} (G) \leq 2 m p (G) + 3$ for any graph…