Secure Integer Domination in Generalized Petersen Graphs.

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Bibliographic Details
Title:	Secure Integer Domination in Generalized Petersen Graphs.
Authors:	L., Gowtham Priya¹ gowthampriya.28@gmail.com, K. A., Venkatesh² ka.venkatesh@alliance.edu.in
Source:	IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2817-2822. 6p.
Subjects:	Petersen graphs, Dominating set, Graph theory, Regular graphs
Abstract:	Secure integer domination is a strengthening of classical domination that combines the concepts of integer domination and secure domination. In this paper we investigate the secure integer domination number of regular graphs, with particular focus on generalized Petersen graphs P(n, k). Using a double counting argument on closed neighborhoods, we establish a general lower bound for an r-regular graph G of order n:We also characterize the case of equality in terms of balanced closed neighborhood sums. As an application, the results are specialized to cubic graphs and generalized Petersen graphs, for which explicit values and bounds of the secure integer domination number are obtained. These results extend known relationships between classical domination, secure domination, and integer domination in structured graphs. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Secure integer domination is a strengthening of classical domination that combines the concepts of integer domination and secure domination. In this paper we investigate the secure integer domination number of regular graphs, with particular focus on generalized Petersen graphs P(n, k). Using a double counting argument on closed neighborhoods, we establish a general lower bound for an r-regular graph G of order n:We also characterize the case of equality in terms of balanced closed neighborhood sums. As an application, the results are specialized to cubic graphs and generalized Petersen graphs, for which explicit values and bounds of the secure integer domination number are obtained. These results extend known relationships between classical domination, secure domination, and integer domination in structured graphs. [ABSTRACT FROM AUTHOR]
ISSN:	19929978