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

{(3,4),4}-富勒烯图的极大共振性

作　　者：YANG Rui MA Yan-fei 杨瑞;马燕菲(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454003,China)

机构地区：[1]School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454003,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第1期1-17,共17页数学季刊(英文版)

基　　金：Supported by NSFC(Grant Nos.11801148 and 11626089);the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。

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.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.

关 键 词：{(3 4) 4}-Fullerene graph k-Resonant Maximally resonant 

分 类 号：O157.6[理学—数学]