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Edge adding stability of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 تیر 1404 اصل مقاله (369.29 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30108.2313 | ||
| نویسندگان | ||
| Arnfried Kemnitz* ؛ Massimiliano Marangio | ||
| Department of Mathematics, Technical University, Braunschweig, Germany | ||
| چکیده | ||
| For an arbitrary invariant $\rho(G)$ of a graph $G$ the $\rho$-edge adding stability number $eas_{\rho}(G)$ is the minimum number of edges of the complement $\overline{G}$ whose addition to $G$ results in a graph $H \supseteq G$ with $\rho(H) \neq \rho(G)$. If such an edge set does not exist, then we set $eas_{\rho}(G) = \infty$. In the first part of this paper we give some general results for $eas_{\rho}(G)$. We prove among others a Gallai's theorem type result for invariants that are based on the $\rho$-edge adding stability number. | ||
| کلیدواژهها | ||
| edge stability number؛ edge adding stability number؛ graph invariant | ||
| مراجع | ||
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[1] S. Akbari, A. Beikmohammadi, B. Brešar, T. Dravec, M.M. Habibollahi, and N. Movarraei, On the chromatic edge stability index of graphs, European J. Combin. 111 (2023), Article ID: 103690. https://doi.org/10.1016/j.ejc.2023.103690
[2] S. Akbari, A. Beikmohammadi, S. Klavar, and N. Movarraei, On the chromatic vertex stability number of graphs, European J. Combin. 102 (2022), Article ID: 103504. https://doi.org/10.1016/j.ejc.2021.103504
[3] S. Akbari, J. Haslegrave, M. Javadi, N. Nahvi, and H. Niaparast, Tight bounds on the chromatic edge stability index of graphs, Discrete Math. 347 (2024), no. 4, Article ID: 113850. https://doi.org/10.1016/j.disc.2023.113850
[4] S. Akbari, S. Klavar, N. Movarraei, and M. Nahvi, Nordhaus–Gaddum and other bounds for the chromatic edge-stability number, European J. Combin. 84 (2020), Article ID: 103042. https://doi.org/10.1016/j.ejc.2019.103042
[5] S. Alikhani and M.R. Piri, On the edge chromatic vertex stability number of graphs, AKCE Int. J. Graphs Comb. 20 (2023), no. 1, 29–34. https://doi.org/10.1080/09728600.2022.2149367
[6] D. Bauer, F. Harary, J. Nieminen, and C.L. Suffel, Domination alteration sets in graphs, Discrete Math. 47 (1983), 153–161. https://doi.org/10.1016/0012-365X(83)90085-7
[7] B. Brešar, S. Klavar, and N. Movarraei, Critical graphs for the chromatic edge-stability number, Discrete Math. 343 (2020), no. 6, Article ID: 111845. https://doi.org/10.1016/j.disc.2020.111845
[8] T. Gallai, Über extreme Punkt- und Kantenmengen (German), Ann. Univ. Sci. Budapest. Eótvós Sect. Math. 2 (1959), 133–138.
[9] F. Harary, Changing and unchanging invariants for graphs, Bull. Malaysian Math. Soc. 5 (1982), 73–78.
[10] T.W. Haynes, L.M. Lawson, R.C. Brigham, and R.D. Dutton, Changing and unchanging of the graphical invariants: minimum and maximum degree, maximum clique size, node independence number and edge independence number, Congr. Numer. 72 (1990), 239–252.
[11] A. Kemnitz and M. Marangio, On the $rho$-subdivision number of graphs., Discuss. Math. Graph Theory 43 (2023), no. 4, 979–997. https://doi.org/10.7151/dmgt.2412
[12] A. Kemnitz and M. Marangio, On the $rho$-edge stability number of graphs, Discuss. Math. Graph Theory 42 (2022), no. 1, 249–262. https://doi.org/10.7151/dmgt.2255
[13] A. Kemnitz and M. Marangio, On the total chromatic edge stability number and the total chromatic subdivision number of graphs, Discrete Math. Lett 10 (2022), 1–8. https://doi.org/10.47443/dml.2021.111
[14] A. Kemnitz and M. Marangio, A Gallai’s theorem type result for the edge stability of graphs, Discrete Math. Lett. 12 (2023), 118–121. https://doi.org/10.47443/dml.2023.088
[15] A. Kemnitz and M. Marangio, On the vertex stability number of graphs, Discrete Appl. Math. 344 (2024), 1–9. https://doi.org/10.1016/j.dam.2023.11.008 [16] A. Kemnitz, M. Marangio, and N. Movarraei, On the chromatic edge stability number of graphs, Graphs Combin. 34 (2018), 1539–1551. https://doi.org/10.1007/s00373-018-1972-y
[17] W. Staton, Edge deletions and the chromatic number, Ars Combin. 10 (1980), 103–106. | ||
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