首页|Maximal Resonance of {(3,4),4}-Fullerene Graphs
Maximal Resonance of {(3,4),4}-Fullerene Graphs
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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 S6,S8,S210,S212,S412,S512,S314,S514,S316,S416,S518,S24 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.
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