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On the number of matchings of graphs formed by a graph operation

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Abstract

Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a,b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.

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Authors and Affiliations

  1. School of Sciences, Jimei University, Xiamen, 361021, China

    Yan Weigen

  2. Institute of Mathematics, Academia Sinica, Taipei, 11529, China

    Yan Weigen & Yeh Yeong-Nan

Authors
  1. Yan Weigen
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  2. Yeh Yeong-Nan
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Correspondence to Yan Weigen.

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Yan, W., Yeh, YN. On the number of matchings of graphs formed by a graph operation. SCI CHINA SER A 49, 1383–1391 (2006). https://doi.org/10.1007/s11425-006-2014-4

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  • DOI: https://doi.org/10.1007/s11425-006-2014-4

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