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New class of integral bipartite graphs with large diameter | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 7، شماره 1، خرداد 2018، صفحه 13-17 اصل مقاله (446.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2016.20738 | ||
| نویسندگان | ||
| Alireza Fiuj Laali* ؛ Hamid Haj Seyyed Javadi | ||
| Shahed university, Tehran, Iran. | ||
| چکیده | ||
| In this paper, we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters. In fact, for every finite set $A$ of positive integers of size $k$ we construct an integral bipartite graph $G$ of diameter $2k$ such that the set of positive eigenvalues of $G$ is exactly $A$. This class of integral bipartite graphs has never found before. | ||
| کلیدواژه‌ها | ||
| Integral graph؛ Diameter؛ root | ||
| مراجع | ||
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[1] A. E. Brouwer and W. H. Haemers, Spectra of graphs, Universitext, Springer, New York, 2012.
[2] P. Csikvári, Integral trees of arbitrarily large diameters, J. Algebraic Combin., 32 (2010) 371–377.
[3] D. Cvetkovi´c, P. Rowlinson and S. Simi´c, An Introduction to the Theory of Graph Spectra, 75, Cambridge University Press, Cambridge, 2010. [4] E. Ghorbani, A. Mohammadian and B. Tayfeh-Rezaie, Integral trees of odd diameters, J. Graph Theory, 70 (2012) 332–338. [5] F. Harary and A. J. Schwenk, Which graphs have integral spectra?, Graphs and Combinatorics, Lecture Notes in Math., 406, Springer, Berlin, (1974) 45–51.
[6] M. Watanabe and A. J. Schwenk, Integral starlike trees, J. Austral. Math. Soc. Ser. A, 28 (1979) 120–128. | ||
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