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arXiv · 2608.14690

The Dual-Server Domination Number of Some Graph Operations

Shrilaxmi Laxminarayana Rao·Sayinath Udupa N. V.·Prathviraj N
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Abstract

A subset $S \subseteq V(G)$ is called a dual-server dominating set if there exists a partition $\pi_S=\{R,B\}$ of $S$ such that every vertex in $V(G)\setminus S$ has at least one neighbour in $R$ and at least one neighbour in $B.$ The minimum cardinality of a DS-dominating set of $G$ is called the dual-server domination number, denoted by $\gamma_{ds}(G)$. In this paper, we investigate the dual-server domination number of several graph operations. We establish exact values for the dual-server domination number of the join, Cartesian product, and corona of graphs. We also determine the dual-server domination number of the splitting graphs of paths, cycles, and complete bipartite graphs. These results extend the study of dual-server domination and provide further insight into its behaviour under graph operations.

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Shrilaxmi Laxminarayana Rao, Sayinath Udupa N. V., Prathviraj N. 2026-08-07. The Dual-Server Domination Number of Some Graph Operations. https://arxiv.org/abs/2608.14690

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