SPECTRA OF GRAPH OPERATIONS BASED ON SPLITTING GRAPH

Zhiqin Lu; Xiaoling Ma; Minshao Zhang

doi:10.11948/20210446

2023 Volume 13 Issue 1

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Zhiqin Lu, Xiaoling Ma, Minshao Zhang. SPECTRA OF GRAPH OPERATIONS BASED ON SPLITTING GRAPH[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 133-155. doi: 10.11948/20210446

Citation:

Zhiqin Lu, Xiaoling Ma, Minshao Zhang. SPECTRA OF GRAPH OPERATIONS BASED ON SPLITTING GRAPH[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 133-155. doi: 10.11948/20210446

SPECTRA OF GRAPH OPERATIONS BASED ON SPLITTING GRAPH

1.
College of Mathematics and System Sciences, Xinjiang University, 830046, Urumqi, China

Corresponding author: Email: mxling2018@163.com(X. Ma)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 12161085), Natural Science Foundation of Xinjiang Province (2021D01C069), Youth Talent Project of Xinjiang Province (2019Q016) and Scientific Research Plan of Universities in Xinjiang, China (XJEDU2021I001)

Abstract

Abstract

The splitting graph $ SP(G) $ of a graph $ G $ is the graph obtained from $ G $ by taking a new vertex $ u' $ for each $ u \in V(G) $ and joining $ u' $ to all vertices of $ G $ adjacent to $ u $. For a connected regular graph $ G_1 $ and an arbitrary regular graph $ G_2 $, we determine the adjacency (respectively, Laplacian and signless Laplacian) spectra of two types of graph operations on $ G_1 $ and $ G_2 $ involving the $ SP $-graph of $ G_1 $. Moreover, applying these results we construct some non-regular simultaneous cospectral graphs for the adjacency, Laplacian and signless Laplacian matrices, and compute the Kirchhoff index and the number of spanning trees of the newly constructed graphs.
- Adjacency spectrum /
- Laplacian spectrum /
- signless Laplacian spectrum /
- cospectral graphs /
- Kirchhoff index /
- the number of spanning trees
MSC: 05C50

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References

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