笛卡尔乘积图的一般位置数  

On the General Position Number of Cartesian Product Graphs

作　　者：田静[1] 许克祥 TIAN Jing;XU Kexiang(School of Mathematics,Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学数学学院,江苏南京210016

出　　处：《集美大学学报（自然科学版）》2023年第3期273-278,共6页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金项目(12271251);江苏省科研与创新项目(KYCX22-0323);南京航空航天大学引航计划项目(KXKCXJJ202204)。

摘　　要：对于图G及子集R V(G),若R的任意三元子集在图G中均是非测地的,则R是图G的一般位置集。图G的最大一般位置集的基数称为G的一般位置数。给出树与任意图的笛卡尔乘积图的一般位置数的下界,验证下界的紧性,并得到星与圈的笛卡尔乘积图的一般位置数的确切值。此外,还得到含通用点且其不在最大一般位置集中的两个图的笛卡尔乘积的一般位置数的下界。For a graph G with R V(G),R is a general position set of G if any triple set of R is non-geodesic in G.The general position number of G is the cardinality of a largest general position set in G.A lower bound on the general position number was determined for the Cartesian product of tree and any connected graph and the sharpness of this lower bound was also verified.The exact value of general position number of the Cartesian product of star and cycle was obtained.Moreover,a lower bound on the general position number was provided of the Cartesian product of two graphs each of which had a universal vertex excluded in their any largest general position sets.

关 键 词：一般位置集 一般位置数 笛卡尔乘积 星 

分 类 号：O157.6[理学—数学]