Imprimitivity index of the adjacency matrix of digraphs

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• 作者：Saieed Akbari^a ; ^{s_akbari@sharif.edu} ; Amir Hossein Ghodrati^a ; ^b ; ^{ghodrati_ah@mehr.sharif.ir} ; Mohammad Ali Hosseinzadeh^c ; ^{ma.hosseinzadeh@modares.ac.ir}
• 关键词：05C20 ; 05C50 ; 15A18
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：517
• 期：Complete
• 页码：1-10
• 全文大小：297 K
• 卷排序：517

文摘

Let G be a graph. An edge orientation of G is called smooth if the in-degree and the out-degree of every vertex differ by at most one. In this paper, we show that if G   is a 2-edge-connected non-bipartite graph with δ(G)≥3δ(G)≥3, then G   has a smooth primitive orientation. Among other results, using the spectral radius of digraphs, we show that if D1D1 is a primitive regular orientation and D2D2 is a non-regular orientation of a given graph, then for sufficiently large t, the number of closed walks of length t   in D1D1 is more than the number of closed walks of length t   in D2D2.