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A Spectral Condition for the Existence of the Square of a Path

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Abstract

Let \(P_k\) be the path of order k. The square \(P_k^2\) of \(P_k\) is obtained by joining all pairs of vertices with distance no more than two in \(P_k\). A graph is called H-free if it does not contain H as a subgraph. In this paper, we consider a Brualdi-Solheid-Turán type problem for \(P_5^2\)-free graphs, and determine the maximum spectral radius among \(P_5^2\)-free graphs of order n.

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  • 01 September 2022

    The original version is updated due to changes in spacing and font

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Acknowledgements

Yanhua Zhao gratefully acknowledge the support of this work by the China Scholarship Council (CSC) (No. 202106740049). The authors would like to thank the reviewers for their careful reading and valuable comments.

Funding

This work was supported in part by the National Natural Science Foundation of China (Grant numbers 11771141 and 12011530064), and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant number NRF-2020R1A2C1A01101838).

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Authors and Affiliations

  1. School of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Yanhua Zhao

  2. Department of Mathematics, Kyungpook National University, Daegu, 41566, Republic of Korea

    Yanhua Zhao & Jongyook Park

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  1. Yanhua Zhao
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  2. Jongyook Park
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Correspondence to Jongyook Park.

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Zhao, Y., Park, J. A Spectral Condition for the Existence of the Square of a Path. Graphs and Combinatorics 38, 126 (2022). https://doi.org/10.1007/s00373-022-02529-4

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