外平面图的(2,1)-点面标号问题

(2,1)-coupled labeling problem of outerplanar graphs

围绕外平面图的(2,1)-点面标号问题展开研究,侧重探索了该标号下外平面图结构性质,证明了:若G为只含有一个闭内面的2-连通外平面图,且该闭内面是一个偶面,那么λvf-2(G)=6当且仅当G是坏的.该成果部分解决了外平面图的(2,1)-点面标号数的刻画问题.

It was discussed the(2,1)-coupled labeling problem of outerplanar graphs.Based on the analysis of outerplanar graphs structure and feature under the(2,1)-coupled labeling,it was proved that:if 2-connected outerplanar graph G contained an unique closed inner face,which was an even face,thenλvf-2(G)=6 if and only if G was bad.The result partially solved the characterization problem of(2,1)-coupled labeling number for outerplanar graphs.