Domination in the Sierpi\'nski graphs S(K_n,t)
Chia-An Liu
TL;DR
This paper investigates various domination parameters in Sierpiński graphs S(K_n,t), providing exact values for domination, Roman domination, and double Roman domination numbers, and confirming the tightness of previous bounds.
Contribution
It introduces a minimal dominating set for Sierpiński graphs and derives exact domination numbers, extending and generalizing existing bounds and results.
Findings
Exact domination numbers for S(K_n,t)
Exact Roman domination numbers for S(K_n,t)
Exact double Roman domination numbers for S(K_n,t)
Abstract
Different types of domination on the Sierpi\'nski graphs S(K_n,t) will be studied in this paper. More precisely, we propose a minimal dominating set for S(K_n,t) so that the exact values of their domination numbers, Roman domination numbers, and double Roman domination numbers are given. As applications, some previous bounds and results are confirmed to be tight and further generalized.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph theory and applications