TY - JOUR
T1 - The spectrum of the edge corona of two graphs
AU - Hou, Yaoping
AU - SHIU, Wai Chee
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2010/9
Y1 - 2010/9
N2 - Given two graphs G1, with vertices 1, 2,., n and edges e1, e2,..., em, and G2, the edge corona G1 {lozenge, open} G2 of G1 and G2 is defined as the graph obtained by taking m copies of G2 and for each edge ek = ij of G, joining edges between the two end-vertices i, j of ek and each vertex of the k-copy of G2. In this paper, the adjacency spectrum and Laplacian spectrum of G1 G2 are given in terms of the spectrum and Laplacian spectrum of G1 and G2, respectively. As an application of these results, the number of spanning trees of the edge corona is also considered.
AB - Given two graphs G1, with vertices 1, 2,., n and edges e1, e2,..., em, and G2, the edge corona G1 {lozenge, open} G2 of G1 and G2 is defined as the graph obtained by taking m copies of G2 and for each edge ek = ij of G, joining edges between the two end-vertices i, j of ek and each vertex of the k-copy of G2. In this paper, the adjacency spectrum and Laplacian spectrum of G1 G2 are given in terms of the spectrum and Laplacian spectrum of G1 and G2, respectively. As an application of these results, the number of spanning trees of the edge corona is also considered.
KW - Adjacency matrix
KW - Corona of graphs
KW - Laplacian matrix
KW - Spectrum
UR - http://www.scopus.com/inward/record.url?scp=78549261793&partnerID=8YFLogxK
U2 - 10.13001/1081-3810.1395
DO - 10.13001/1081-3810.1395
M3 - Journal article
AN - SCOPUS:78549261793
SN - 1081-3810
VL - 20
SP - 586
EP - 594
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
ER -