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Spectra of Subdivision Vertex-Edge Join of Three Graphs.
- Source :
-
Mathematics (2227-7390) . Feb2019, Vol. 7 Issue 2, p171. 1p. - Publication Year :
- 2019
-
Abstract
- In this paper, we introduce a new graph operation called subdivision vertex-edge join (denoted by G 1 S ▹ (G 2 V ∪ G 3 E) for short), and then the adjacency spectrum, the Laplacian spectrum and the signless Laplacian spectrum of G 1 S ▹ (G 2 V ∪ G 3 E) are respectively determined in terms of the corresponding spectra for a regular graph G 1 and two arbitrary graphs G 2 and G 3 . 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 of G 1 S ▹ (G 2 V ∪ G 3 E) whenever G i are regular graphs for each index i = 1 , 2 , 3 . As applications, we construct infinitely many pairs of A-cospectral mates, L-cospectral mates, Q-cospectral mates and L -cospectral mates. Finally, we give the number of spanning trees, the (degree-)Kirchhoff index and the Kemeny's constant of G 1 S ▹ (G 2 V ∪ G 3 E) , respectively. [ABSTRACT FROM AUTHOR]
- Subjects :
- *REGULAR graphs
*GEOMETRIC vertices
*SPANNING trees
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 7
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 135604300
- Full Text :
- https://doi.org/10.3390/math7020171