关于任意零元阿贝尔有限模可加图群及其在信息安全中的应用  

On every-zero Abelian finite-modular additive graphic groups and its application in information security

作　　者：赵梅梅[1] 姚兵 ZHAO Mei-mei;YAO Bing(College of Science, Gansu Agricultural University, Lanzhou 730070, China;College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

机构地区：[1]甘肃农业大学理学院,甘肃兰州730070 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《广州大学学报（自然科学版）》2022年第1期27-33,共7页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61363060,61662066)。

摘　　要：文章定义了(q+1)-模(负)优美标号和混合优美标号,基于这些新标号建立了任意零元阿贝尔有限模可加图群。给出了(q+1)-模混合优美图可以生成的图群和图子群及它们的阶。提出了每个(q+1)-模优美图可以生成顶点模图,每个顶点模图又可以生成边模图,这些顶点模图和边模图构成了任意零元阿贝尔有限模可加图群。对于(q+1)-模负优美图和(q+1)-模混合优美图也得到了类似的结果。此外,给出了任意零元阿贝尔有限模可加图群对网络整体加密的例子。The(q+1)-modular(negative)graceful labelling and mixed graceful labelling are defined.Based on these new labellings,the every-zero Abelian finite-modular additive graphic groups are established.The graphic groups and subgroups that can be generated and their orders are given when the graph is a(q+1)-modular mixed graceful graph.It is proposed that each(q+1)-modular graceful graph can generate vertex-modular graphs,each vertex-modular graph can generate edge-modular graphs,and these vertex-modular graphs and edge-modular graphs can form every-zero Abelian finite-modular additive graphic groups.Similar results are obtained for(q+1)-modular negative graceful graph and(q+1)-modular mixed graceful graph.Moreover,an example is given for the application of the every-zero Abelian finite-modular additive graphic groups to integral network encryption.

关 键 词：图形密码 任意零元阿贝尔有限模可加图群 优美标号 边模图 顶点模图 

分 类 号：O157.5[理学—数学]