Year: 2026
Type: preprint
Abstract: A nonempty vertex set D of a graph is secure if and only if, for every nonempty subset X of D, the closed neighborhood of X contains at least as many vertices of D as vertices outside D. A secure dominating set is a set that is both secure and dominating, and the secure domination number is the minimum cardinality of such a set. Previous work determined the secure domination number of Sierpinski graphs S_n k for even k and for odd k when n = 2. The exact values for odd k and n\geq3 remained open. In this paper, we determine these remaining values.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G8987426777
OpenAlex ID: W7223124195