Lower bounds on the Security number of the Cartesian product of graphs

P Asha; M R Chithra

doi:10.1142/s1793830926500680

June 4, 2026Discrete Mathematics Algorithms and Applications

Lower bounds on the Security number of the Cartesian product of graphs

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Key Points

This research aims to characterize graphs where the security number of the Cartesian product equals the sum of the security numbers of the individual graphs and establish lower bounds.
Characterization of graphs with the relation s(G☐H) = s(G) + s(H).
Derivation of lower bounds for the security number on Cartesian products of connected graphs.
Identified specific graph structures that satisfy the equality condition for security numbers.
Established lower bounds on the security numbers for various configurations of connected graphs.

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Implication

Characterizes graph security numbers and establishes lower bounds for Cartesian products.

Abstract

A secure set of a graph is a set of vertices that can defend against attacks from the neighbourhood to any of its subsets. The security number of a graph is the minimum cardinality of a secure set. In this paper, we have characterised the graphs with s(G☐H) = s(G) + s(H). Also, we obtain a lower bound on the security number of the Cartesian product of two connected graphs.

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Asha et al. (2026) studied this question.

synapsesocial.com/papers/6a23b9f271a5da9775e75c65 https://doi.org/10.1142/s1793830926500680

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Lower bounds on the Security number of the Cartesian product of graphs

Key Points

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Implication

Abstract

Discussion

Cite This Study

Lower bounds on the Security number of the Cartesian product of graphs

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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