Spectra of Subdivision Vertex-Edge Join of Three Graphs
Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
Authors to whom correspondence should be addressed.
Received: 18 January 2019 / Revised: 2 February 2019 / Accepted: 6 February 2019 / Published: 13 February 2019
In this paper, we introduce a new graph operation called subdivision vertex-edge join
for short), and then the adjacency spectrum
, the Laplacian spectrum
and the signless Laplacian spectrum
are respectively determined in terms of the corresponding spectra for a regular graph
and two arbitrary graphs
. All the above can be viewed as the generalizations of the main results in [X. Liu, Z. Zhang, Bull. Malays. Math. Sci. Soc.
, 2017:1–17]. Furthermore, we also determine the normalized Laplacian spectrum
are regular graphs for each index
. As applications, we construct infinitely many pairs of A-cospectral mates
, L-cospectral mates
, Q-cospectral mates
. Finally, we give the number of spanning trees
, the (degree-
and the Kemeny’s constant
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MDPI and ACS Style
Wen, F.; Zhang, Y.; Li, M. Spectra of Subdivision Vertex-Edge Join of Three Graphs. Mathematics 2019, 7, 171.
Wen F, Zhang Y, Li M. Spectra of Subdivision Vertex-Edge Join of Three Graphs. Mathematics. 2019; 7(2):171.
Wen, Fei; Zhang, You; Li, Muchun. 2019. "Spectra of Subdivision Vertex-Edge Join of Three Graphs." Mathematics 7, no. 2: 171.
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