Variants of the domination number for flower snarks (Q6597991)

This paper investigates variants of the domination number for the infinite family of flower snarks \( J_n \), a well-known class of cubic graphs. Flower snarks are of particular interest due to their 3-regularity and non-3-edge-colorability. The authors extend the current understanding by determining several domination-related parameters for \( J_n \), including the independent domination number, 2-domination number, total domination number, connected domination number, secure domination number, and weak Roman domination number.\N\NA key contribution is the derivation of exact formulas and bounds for these domination parameters as functions of \( n \), accompanied by rigorous proofs, often utilizing induction and configurations. The study is relevant for researchers interested in graph theory, specifically those working on domination, snarks, or 3-regular graphs.