The normalized Laplacians on both k-triangle graph and k-quadrilateral graph with their applications

Jing Huang and Shuchao Li

Applied Mathematics and Computation, 2018, vol. 320, issue C, 213-225

Abstract: The k-triangle graph Tk(G) is obtained from a graph G by replacing each edge in G with k+1 parallel paths, in which one is of length 1 and each of the rest k paths is of length 2; whereas the k-quadrilateral graph Qk(G) is obtained from G by replacing each edge in G with k+1 parallel paths, in which one is of length 1 and each of the rest k paths is of length 3. In this paper, we completely determine the normalized Laplacian spectrum on Tk(G) (resp. Qk(G)) for any connected graph G, k ⩾ 2. As applications, the correlation between the degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Tk(G) (resp. Qk(G), the r-th iterative k-triangle graph Trk(G), the r-th iterative k-quadrilateral graph Qrk(G)) and those of G are derived. Our results extend those main results obtained in Xie et al. (2016) and Li and Hou (2017).

Keywords: Normalized Laplacian; Degree-Kirchhoff index; Kemeny’s constant; Spanning tree (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:213-225

DOI: 10.1016/j.amc.2017.09.035

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