数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 1-17.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.001

• •    下一篇

富勒烯图的极大共振性

杨瑞, 马燕菲   

  1. (School of Mathematics and Information Science, Henan Polytechnic University,
    Jiaozuo 454003, China
  • 收稿日期:2022-07-08 出版日期:2024-03-30 发布日期:2024-03-30
  • 通讯作者: YANG Rui (1983-), female, native of Nanyang, Henan, lecturer of Henan Polytechnic University, engages in graph theory and matching theory. E-mail:yangrui@hpu.edu.cn
  • 作者简介: YANG Rui (1983-), female, native of Nanyang, Henan, lecturer of Henan Polytechnic University, engages in graph theory and matching theory; MA Yan-fei (1997-), female, native of Nanyang, Henan, graduate student of Henan Polytechnic University, engages in graph theory and matching theory.
  • 基金资助:
     Supported by NSFC (Grant Nos. 11801148 and 11626089) and the Foundation for the
    Doctor of Henan Polytechnic University (Grant No. B2014-060).

Maximal Resonance of {(3,4),4}-Fullerene Graphs

YANG Rui, MA Yan-fei   

  1. (School of Mathematics and Information Science, Henan Polytechnic University,
    Jiaozuo 454003, China
  • Received:2022-07-08 Online:2024-03-30 Published:2024-03-30
  • Contact: YANG Rui (1983-), female, native of Nanyang, Henan, lecturer of Henan Polytechnic University, engages in graph theory and matching theory. E-mail:yangrui@hpu.edu.cn
  • About author: YANG Rui (1983-), female, native of Nanyang, Henan, lecturer of Henan Polytechnic University, engages in graph theory and matching theory; MA Yan-fei (1997-), female, native of Nanyang, Henan, graduate student of Henan Polytechnic University, engages in graph theory and matching theory.
  • Supported by:
     Supported by NSFC (Grant Nos. 11801148 and 11626089) and the Foundation for the
    Doctor of Henan Polytechnic University (Grant No. B2014-060).

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摘要： A {(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4. It follows from Euler’s formula that the number of triangular faces is eight. A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating. Let k be a positive integer, S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern. Moreover, if graph S is k-resonant for any integer k, then S is called maximally resonant.

关键词: {(3,4),4}-Fullerene graph, k-Resonant, Maximally resonant

Abstract: A {(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4. It follows from Euler’s formula that the number of triangular faces is eight. A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating. Let k be a positive integer, S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern. Moreover, if graph S is k-resonant for any integer k, then S is called maximally resonant.

Key words: {(3,4),4}-Fullerene graph, k-Resonant, Maximally resonant

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