仙人掌图和卡氏积图的连通包数  

CONNECTED HULL NUMBERS OF CACTUS GRAPHS AND CARTESIANPRODUCT GRAPHS

作　　者：贾倩琼 陈春霖 秦文文 马儇龙 JIA Qianqiong;CHEN Chunlin;QIN Wenwen;MA Xuanlong(School of Science,Xi'an Shiyou University,Xi'an,Shanxi 710065,China)

机构地区：[1]西安石油大学理学院,陕西西安710065

出　　处：《井冈山大学学报（自然科学版）》2024年第4期1-6,共6页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(12326333)。

摘　　要：测地线的概念起源于几何学、拓扑学及函数分析中的凸集理论,它在选址问题、网络设计及控制理论等方面有重要意义。在图论中定义了凸性后,测地线问题及与之相关的测地数问题成为揭示图的结构性质的一个重要指标及参数。图的连通包数是定义在图中测地线上的一个参数。针对计算图的连通包数问题,本研究用组合分析法确定了仙人掌图C_(n)·C_(n)及卡氏积图P_(m)×K_(2)、P_(m)×C_(3)、P_(2)×C_(n)的连通包数,其中m≥2,n≥3,P_(m)是长度为m-1的路,C_(n)是长度为n的圈。The concept of geodesic originated from convex set theory in geometry,topology,and function analysis.It has important significance in location selection problems,network design,and control theory.After defining convexity in graph theory,geodesic problems and related geodesic number problems become important indicators and parameters for revealing the structural properties of graphs.The connected hull number of a graph is a parameter defined on the geodesics in the graph.For the question of calculating the connected hull number in a graph,this paper determines the connected hull numbers of the cactus graph n n C_(n)·C_(n),Cartesian product graphs P_(m)×K_(2)、P_(m)×C_(3)、P_(2)×C_(n),where m≥2,n≥3,P_(m)is the path of length m-1,and C_(n)is the cycle of length n.

关 键 词：凸集 连通包集 连通包数 仙人掌图 卡氏积 

分 类 号：O157.5[理学—数学]