Sandip Das

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cs.DM2025

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 $I^_{b}^{3} (G)$ is the broadcast domination number. It is known that $m p (G) \leq I^_{b}^{3} (G)$ and $I^_{b}^{3} (G) \leq 2 m p (G) + 3$ for any gra…

cs.DM2025

On the Cop Number of String Graphs

Sandip Das, Harmender Gahlawat

Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The \emph{cop number} of a graph is the mini…