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  • Effect of an edge subdivision on game domination numbers
    Dokyeesun, Pakanun ; Worawannotai, Chalermpong
    Domination game is a game on a graph ▫$G$▫ played by two players called Dominator and Staller. They alternately choose vertices of ▫$G$▫ such that each move dominates at least one new undominated ... vertex. The game ends when all vertices are dominated. Dominator's goal is to finish the game as soon as possible, while Staller's goal is to prolong it as much as she can. When Dominator moves first, the game is a Dominator-start game; when Staller moves first, it is a Staller-start game. The game domination numbers ▫$\gamma_g(G)$▫ and ▫$\gamma'_g(G)$▫ are the sizes of the final dominating sets when both players play optimally for the Dominator-start game and for the Staller-start game, respectively. For a graph ▫$G$▫ and an edge ▫$e$▫, we show that ▫$0\leq \gamma_g(G) - \gamma_g(Ge)\leq 2$▫ and ▫$0\leq\gamma'_g(G) - \gamma'_g(Ge)\leq 2$▫, where ▫$G_e$▫ is is the graph resulting from subdividing the edge ▫$e$▫ in ▫$G$▫. We also demonstrate that each difference satisfying the above bounds are realizable by infinitely many connected graphs.
    Vir: Asian-European journal of mathematics. - ISSN 1793-5571 (Vol. 13, no. 7, 2020, art. 2050130 (17 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 87831043

    Povezava(-e):

    https://www.worldscientific.com/doi/abs/10.1142/S1793557120501302
    DOI

vir: Asian-European journal of mathematics. - ISSN 1793-5571 (Vol. 13, no. 7, 2020, art. 2050130 (17 str.))
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