两类冠图的Randi■能量

详细信息    查看全文 | 推荐本文 |

英文篇名：Randi■ energy of two classes of corona graphs 作者：付飞琴 ; 邵燕灵 英文作者：FU Feiqin;SHAO Yanling;School of Science, North University of China; 关键词：Randi■矩阵 ; Randi■能量 ; 冠图 ; 图谱 英文关键词：Randi■ matrix;;Randi■ energy;;corona;;graph spectrum 中文刊名：HZSZ 英文刊名：Journal of Central China Normal University(Natural Sciences) 机构：中北大学理学院; 出版日期：2019-07-23 出版单位：华中师范大学学报(自然科学版) 年：2019 期：v.53;No.186 基金：山西省自然科学基金项目(201601D202003);; 中北大学理学院研究生创新科研项目(20180808) 语种：英文; 页：HZSZ201904002 页数：5 CN：04 ISSN：42-1178/N 分类号：12-15+24

摘要

设G是顶点集为V(G)={v_1,v_2,…,v_n}的简单无向图,R(G)=(r_(ij))是图G的Randi■矩阵,其中当v_i与v_j相邻时r_(ij)=1/■;否则r_(ij)=0.图G的Randi■能量RE(G)指R(G)的特征值的绝对值之和.冠图G■_1G_2是由图G_1的每个顶点与图G_2的一个拷贝的所有顶点相连得到的.本文对冠图I_r(K_n)和K■_nK_m的Randi■能量进行了研究.
        Let Gbe a simple undirected graph,with vertex setV(G)={v_1,v_2,…,v_n}.The Randi■ matrix of Gis the matrix R(G)=(r_(ij)),where r_(ij)=1/■ if the vertices v_i and v_j are adjacent and r_(ij)=0 otherwise.The Randi■ energy RE(G)is the sum of absolute values of the eigenvalues of R(G).The corona of G■_1G_2 is obtained by connecting each vertex of G_1to all vertices of a copy of G_2.In this paper,the Randic'energy of corona graphs I_r(K_n)and K■_nK_m are studied.

引文

[1]BONDY J A,MURTY U S R.Graph Theory[M].New York:Springer,2008.
    [2]RANDIC'M.On characterization of molecular branching[J].Journal of the American Chemical Society,1975,97(23):6609-6615.
    [3]BOZKURT ■B,G■NG■R A D,GUTMAN I,etal.Randi■ matrixand Randi■ energy[J].Match Communications in Mathematical and in Computer Chemistry,2010,64:239-250.
    [4]GUTMAN I,FURTULA B,BOZKURT■B.On Randi■ energy[J].Linear Algebra and it's Applications,2014,442:50-57.
    [5]ALIKHANI S,GHANBARIN.Randi■ energy of specific graphs[J].Applied Mathematics and Computation,2015,269:722-730.
    [6]REDDY P S K,PRAKASHA K N,SIDDALINGASWAMYV M.Minimum dominating Randic energy of a graph[J].Department of Mathematics,2017,19(2):28-35.
    [7]GLOGI■E,ZOGI■E,GLI■OVI■N.Remarks on the upper bound for the Randi■ energy of bipartite graphs[J].Discrete Applied Mathematics,2017,221:67-70.
    [8]BARIK S,PATI S,SARMA B K.The spectrum of the corona of two graphs[J].Siam Journal on Discrete Mathematics,2007,21(1):47-56.
    [9]刘西奎,李艳.关于冠图的关联着色[J].江苏师范大学学报(自然科学版),2001,19(2):16-18.LIU X K,LI Y.The incidence coloring of corona graph[J].Journal of Jiangsu Normal University(Natural Science Edition),2001,19(2):16-18.(Ch).
    [10]FRITSCHER E,TREVISAN V.Exploring symmetries to decompose matrices and graphs preserving the spectrum[J].Siam Journal on Matrix Analysis and Applications,2016,37(1):260-289.