湖北师范学院学报（自然科学版）
湖北師範學院學報（自然科學版）
호북사범학원학보（자연과학판）
JOURNAL OF HUBEI NORMAL UNIVERSITY(NATURAL SCIENCE)
2013年
3期
28-30
,共3页
硼氮富勒烯图%完美匹配%反强迫数
硼氮富勒烯圖%完美匹配%反彊迫數
붕담부륵희도%완미필배%반강박수
boron-nitrogen fullerene%perfect matching%anti-forcing number
设G是一个有完美匹配的图。若G的边集S满足G-S有唯一完美匹配，则称S为反强迫集。包含边数最少的反强迫集叫做极小反强迫集，其中边的数目叫做图G 的反强迫数。本文主要解决硼氮富勒烯图（恰好有六个四边形面，其它面都是六边形，3-连通的平面二部图）的反强迫数。我们得到一类管状，环边连通度为3的硼氮富勒烯图的反强迫数，然后得到任何硼氮富勒烯图的反强迫数至少为3，进而构造出所有反强迫数为3的硼氮富勒烯图，共有两个。
設G是一箇有完美匹配的圖。若G的邊集S滿足G-S有唯一完美匹配，則稱S為反彊迫集。包含邊數最少的反彊迫集叫做極小反彊迫集，其中邊的數目叫做圖G 的反彊迫數。本文主要解決硼氮富勒烯圖（恰好有六箇四邊形麵，其它麵都是六邊形，3-連通的平麵二部圖）的反彊迫數。我們得到一類管狀，環邊連通度為3的硼氮富勒烯圖的反彊迫數，然後得到任何硼氮富勒烯圖的反彊迫數至少為3，進而構造齣所有反彊迫數為3的硼氮富勒烯圖，共有兩箇。
설G시일개유완미필배적도。약G적변집S만족G-S유유일완미필배，칙칭S위반강박집。포함변수최소적반강박집규주겁소반강박집，기중변적수목규주도G 적반강박수。본문주요해결붕담부륵희도（흡호유륙개사변형면，기타면도시륙변형，3-련통적평면이부도）적반강박수。아문득도일류관상，배변련통도위3적붕담부륵희도적반강박수，연후득도임하붕담부륵희도적반강박수지소위3，진이구조출소유반강박수위3적붕담부륵희도，공유량개。
Let G be a graph that admits a perfect matching M .A anti-forcing set of G is the edge set S such that G-S has a unique perfect matching .The anti-forcing set of the smallest cardinality is called the minimal anti -forcing set , and its car-dinality is the anti-forcing number of G.In this paper, we consider boron-nitrogen (BN) fullerene graphs, cubic 3-con-nected plane bipartite graphs with exactly six square faces and other hexagonal faces .We obtain that the anti -forcing number of tubular BN-fullerene graphs with cyclic edge -connectivity 3.Then we show that the anti -forcing number of any BN -fullerene graphs is at least three .Furthermore, we mainly construct all two BN -fullerene graphs with the anti -forcing num-ber three.
