图的强和与强积导出的距离整谱图  

Distance Integral Graphs Generated by Strong Sum and Strong Product

作　　者：卢俊颖 刘伟俊[1] 鲁卢 Lu Junying;Liu Weijun;Lu Lu(School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《数学理论与应用》2021年第1期33-43,共11页Mathematical Theory and Applications

基　　金：supported by NSFC(Nos.12001544,11671402,11871479)。

摘　　要：对于两个连通图G和H,它们的强和G⊕H是一个点集为V(G)×V(H),边集为{(u,v)(u′,v′)|uu′∈E(G),v=v′}∪{(u,v)(u′,v′)|uu′∈E(G),vv′∈E(H)}的图?它们的强积G■H是一个点集为V(G)×V(H),边集为{(u,v)(u′,v′)|uu′∈E(G),v=v′}∪{(u,v)(u′,v′)|uu′∈E(G),vv′∈E(H)}∪{(u,v)(u′,v′)|u=u′,vv′∈E(H)}的图.当H的直径小于3时,本文完全确定了G⊕H和G■H中的距离.进而,当G和H满足某些条件时,我们得到了G⊕H和G■H的距离谱.作为应用,我们得到了一些由强和与强积导出的距离谱图.特别地,我们得到了一个新的由强积导出的距离整谱图无穷类.For two connected graphs G and H,the strong sum G⊕H is the graph with vertex set V(G)×V(H)and edge set{(u,v)(u′,v′)|uu′∈E(G),v=v′}∪{(u,v)(u′,v′)|uu′∈E(G),vv′∈E(H)},and the strong product G■H is the graph with vertex set V(G)×V(H)and edge set{(u,v)(u′,v′)|uu′∈E(G),v=v′}∪{(u,v)(u′,v′)|uu′∈E(G),vv′∈E(H)}∪{(u,v)(u′,v′)|u=u′,vv′∈E(H)}.In this paper we completely obtain the distances in G⊕H and G■H when H has diameter less than 3.Furthermore,we get the distance spectra of G⊕H and G■H when G and H satisfy some conditions.As applications,some distance integral graphs generated by the strong sum and the strong product are obtained.Especially,we get a new infinite class of distance integral graphs generated by the strong product.

关 键 词：距离谱 距离整谱图 强和 强积 

分 类 号：O157.5[理学—数学]