Variants of the Domination Number for Flower Snarks
Ryan Burdett, Michael Haythorpe, Alex Newcombe

TL;DR
This paper investigates various domination parameters in flower snarks, a class of 3-regular graphs, providing new exact values for multiple domination variants beyond the classical domination number.
Contribution
It extends existing research by determining several new domination parameters for flower snarks, including independent, 2-, total, connected, upper, secure, and weak Roman domination numbers.
Findings
Independent domination number determined for flower snarks.
2-domination and total domination numbers calculated.
Connected and secure domination numbers established.
Abstract
We consider the flower snarks, a widely studied infinite family of 3--regular graphs. For the Flower snark on vertices, it is trivial to show that the domination number of is equal to . However, results are more difficult to determine for variants of domination. The Roman domination, weakly convex domination, and convex domination numbers have been determined for flower snarks in previous works. We add to this literature by determining the independent domination, 2-domination, total domination, connected domination, upper domination, secure Domination and weak Roman domination numbers for flower snarks.
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Taxonomy
TopicsAdvanced Graph Theory Research · Game Theory and Applications
