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The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number

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  • Luozhong Gong
  • Weijun Liu
  • Musavarah Sarwar

Abstract

The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G. In this paper, among the unicyclic graphs of order n, we present the ordering of the unicyclic graphs with matching number 2 according to the λ1G values for n≥11 and also determine the graphs with the first and second largest λ1G values with matching number 3.

Suggested Citation

  • Luozhong Gong & Weijun Liu & Musavarah Sarwar, 2022. "The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, May.
    • Handle: RePEc:hin:jjmath:3589448
    DOI: 10.1155/2022/3589448
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