Coalition of cubic graphs of order at most $10$

Alikhani, Saeid; Golmohammadi, Hamidreza; Konstantinova, Elena V.

doi:10.22049/cco.2023.28328.1507

تعداد نشریات	7
تعداد شماره‌ها	104
تعداد مقالات	1,152
تعداد مشاهده مقاله	1,061,001
تعداد دریافت فایل اصل مقاله	889,098

	Coalition of cubic graphs of order at most $10$
Communications in Combinatorics and Optimization
مقاله 4، دوره 9، شماره 3، آذر 2024، صفحه 437-450 اصل مقاله (422.59 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2023.28328.1507
نویسندگان
Saeid Alikhani^* ¹؛ Hamidreza Golmohammadi²^{، 3}؛ Elena V. Konstantinova²^{، 3}
¹Department of Mathematics, Yazd University, 89195-741.
²Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia
³Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia
چکیده
The coalition in a graph $G$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a dominating set but whose union $V_{1}\cup V_{2}$, is a dominating set. A coalition partition in a graph $G$ is a vertex partition $\pi$ = $\{V_1, V_2,\dots, V_k \}$ such that every set $V_i \in \pi$ is not a dominating set but forms a coalition with another set $V_j\in \pi$ which is not a dominating set. The coalition number $C(G)$ equals the maximum $k$ of a coalition partition of $G$. In this paper, we compute the coalition numbers of all cubic graphs of order at most $10$.
کلیدواژه‌ها
Coalition؛ cubic graphs؛ Petersen graph

مراجع
[1] S. Alikhani, D. Bakhshesh, and H.R. Golmohammadi, Total coalitions in graphs, Available at https://arxiv.org/abs/2211.11590. [2] S. Alikhani and Y.H. Peng, Domination polynomials of cubic graphs of order 10, Turkish J. Math. 35 (2011), no. 3, 355–366. https://doi.org/10.3906/mat-1002-141 [3] D. Bakhshesh, M.A. Henning, and D. Pradhan, On the coalition number of trees, Bull. Malaysian Math. Sci. Soc. 46 (2023), Article number: 95. [4] E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), no. 3, 247–261. https://doi.org/10.1002/net.3230070305 [5] T.W. Haynes, J.T. Hedetniemi, S.T. Hedetniemi, A.A. McRae, and R. Mohan, Introduction to coalitions in graphs, AKCE Int. J. Graphs Combin. 17 (2020), no. 2, 653–659. https://doi.org/10.1080/09728600.2020.1832874 [6] T.W. Haynes, J.T. Hedetniemi, S.T. Hedetniemi, A.A. McRae, and R. Mohan, Upper bounds on the coalition number, Austral. J. Combin. 80 (2021), no. 3, 442–453. [7] T.W. Haynes, J.T. Hedetniemi, S.T. Hedetniemi, A.A. McRae, and R. Mohan, Coalition graphs, Commun. Comb. Optim. 8 (2023), no. 2, 423–430. [8] T.W. Haynes, J.T. Hedetniemi, S.T. Hedetniemi, A.A. McRae, and R. Mohan, Coalition graphs of paths, cycles and trees, Discuss. Math. Graph Theory 43 (2023), no. 4, 931–946. https://doi.org/10.7151/dmgt.2416 [9] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs, Advanced Topics, Marcel Dekker, Inc., New York, 1998. [10] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc. New York, 1998. [11] G.B. Khosrovshahi, Ch. Maysoori, and B. Tayfeh-Rezaie, A note on 3-factorizations of $K_{10}$, J. Combin. Designs 9 (2001), no. 5, 379–383. https://doi.org/10.1002/jcd.1018 [12] B. Zelinka, On domatic numbers of graphs, Math. Slovaca 31 (1981), no. 1, 91–95. [13] B. Zelinka, Domatic number and degrees of vertices of a graph, Math. Slovaca 33 (1983), no. 2, 145–147. [14] B. Zelinka, Domination in the generalized Petersen graphs, Czechoslov. Math. J. 52 (2002), no. 1, 11–16. https://doi.org/10.1023/A:1021759001873
آمار تعداد مشاهده مقاله: 429 تعداد دریافت فایل اصل مقاله: 1,060

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Coalition of cubic graphs of order at most $10$