The normalized Laplacian spectrum of quadrilateral graphs and its applications

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• 作者：Deqiong Li ; Yaoping Hou ; ^{yphou@hunnu.edu.cn} ; ^{yphou9898@gmail.com}
• 关键词：Quadrilateral ; Normalized Laplacian spectrum ; Multiplicative degree-Kirchhoff index ; Kemeny&rsquo ; s constant ; The number of spanning trees
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：297
• 期：Complete
• 页码：180-188
• 全文大小：383 K
• 卷排序：297

文摘

The quadrilateral graph Q(G) of G is obtained from G by replacing each edge in G with two parallel paths of lengths 1 and 3. In this paper, we completely describe the normalized Laplacian spectrum on Q(G) for any graph G. As applications, the significant formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Q(G) and the quadrilateral iterative graph Qr(G) are derived.