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Matching Integral Graphs of Small Order | ||
Journal of New Researches in Mathematics | ||
مقاله 9، دوره 6، شماره 26، آذر و دی 2020، صفحه 99-110 اصل مقاله (873.6 K) | ||
نوع مقاله: research paper | ||
نویسنده | ||
Somayeh Khalashi Ghezelahmad | ||
Faculty member, Department of Mathematics, Science and Research Branch, Islamic Azad , ,University, Tehran, Iran | ||
چکیده | ||
In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matching integral claw-free graph and K_2 is the only connected matching integral graph with a perfect matching. In this work, we characterize mathching integral graphs according to their order. We determine all connected matching integral graphs on at most seven vertices. We show that there are exactly eight matching integral graphs up to seven vertices. In addition, we prove that any connected matching integral graph on eight vertices has a 3-matching and its size is fourteen. Finally, we characterize all connected matching integral graphs with maximum vertex degrees at most three. | ||
کلیدواژهها | ||
Matching؛ Matching polynomial؛ Matching integral graph | ||
مراجع | ||
[1] C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, Inc., 1993.
[2] C.D. Godsil, Algebraic matching theory, Electron. J. Combin., 2 (1995), 1-14.
[3] C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J. Graph Theory, 5(2) (1981), 137-144.
[4] I. Gutman, The matching polynomial, MATCH Commun. Math. Comput. Chem., 6 (1979), 75-91.
[5] I. Gutman and F. Harary, Generalizations of the matching polynomial, Utilitas Math., 24 (1983), 97-106.
[12] C.Y. Ku and W. Chen, An analogue of the Gallai-Edmond structure theorem for non-zero roots of the matching polynomial, J. Combin. Theory Ser. B, 100 (2010), 119-127.
[13] S. Khalashi Ghezelahmad, On matching integral graphs, Mathematical Sciences, 13 (2019), 387–394.
[6] I. Gutman and S. Wagnerb, The matching energy of a graph, Discrete Appl. Math., 160 (2012), 2177-2187.
[7] F. Harary and A.J. Schwenk, Which graphs have integral spectra? Graphs and Combinatorics., Lecture Notes in Math., Springer-Verlag, Berlin, 406 (1974), 45-51.
[8] K.T. Bali ska, D. Cvetkovi , Z. Radosavljevi , S.K. Simi and D. Stevanovi , A survey on integral graphs, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 13 (2002), 42-65.
[9] S. Akbari, P. Csikvári, A. Ghafari, S. Khalashi Ghezelahmad and M. Nahvi, Graphs with integer matching polynomial zeros, Discrete Appl. Math., 224 (2017), 1-8.
[10] O.J. Heilmann and E.H. Lieb, Theory of monomer-dimer systems, Commun. Math. Physics, 25 (1972), 190-232.
[11] E. Ghorbani, Graphs with few matching roots, Graphs Combin. 29 (2013), 1377-1381. | ||
آمار تعداد مشاهده مقاله: 258 تعداد دریافت فایل اصل مقاله: 251 |