Some new classes of distance integral graphs constructed from integral graphs

Journal of Linear and Topological Algebra

دوره 12، شماره 01، خرداد 2023، صفحه 43-47   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.700638

نویسنده

S. M. Mirafzal^*

Department of Mathematics‎, ‎Lorestan University‎, ‎Khoramabad‎, ‎Iran

چکیده

‎The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$‎. ‎A graph is called distance integral if all of its distance eigenvalues are integers‎. ‎In this paper‎, ‎we introduce some new classes of distance integral graphs‎. ‎In particular‎, ‎we show that if $n,k$ are integers such that $n \geq 3k >0$‎, ‎then the bipartite Kneser graph $H(n,k)$ is distance integral‎. ‎Moreover‎, ‎we determine the distance spectrum of $H(n,k)$‎. ‎Also‎, ‎we show that every distance regular integral graph is distance integral‎.

کلیدواژه‌ها

Distance integral؛ vertex-transitive؛ distance regular؛ bipartite Kneser graph

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