张旻劭,马小玲

• 1:新疆大学数学与系统科学学院

摘要(Abstract)：

设G是简单连通图,图G的逆和反度指标定义为■,其中d_u是图G中点u的度.首先考虑任意两个图的图运算,如图连接运算,笛卡儿积运算,对称差运算,字典序积运算,冠运算,接着研究运算后图的逆和反度指标的界,并刻画了极值图.

关键词(KeyWords)： 图运算;逆和反度指标;笛卡儿积;字典序积

Abstract:

Keywords:

基金项目(Foundation): 新疆维吾尔自治区自然科学基金面上项目(2021D01C069);; 新疆维吾尔自治区优秀青年科技人才项目(2019Q016)

作者(Author): 张旻劭,马小玲

DOI: 10.13568/j.cnki.651094.651316.2021.07.03.0001

参考文献(References)：

• [1]BONDY J A,MURTY U S R.Graph theory[M].New York:Springer,2008.
• [2]GU X M,ZHAO B,TANG J J.Polyphenyl chains with extremal Wiener index[J].Journal of Xinjiang University(Natural Science Edition),2010,27(1):32-36.
• [3]ZHANG J X,ZHAO B.Maximizing a class of unicyclic graphs by means of Hosoya index[J].Journal of Xinjiang University(Natural Science Edition),2013,30(4):422-426.
• [4]VUKICEVIC D,GASPEROV M.Bond additive modeling 1 adriatic indices[J].Croatica Chemica Acta,2010,83:243-260.
• [5]FALAHATI-NEZHAD F,AZARI M,DOSLIC T.Sharp bounds on the inverse sum indeg index[J].Discrete Applied Mathematics,2017,217:185-195.
• [6]SEDLAR J,STEVANOVIC D,VASILYEV A.On the inverse sum indeg index[J].Discrete Applied Mathematics,2015,184:202-212.
• [7]MATEJIC M M,MILOVANOVIC I Z,MILOVANOVIC E I.Upper bounds for the inverse sum indeg index of graphs[J].Discrete Applied Mathematics,2018,251:258-267.
• [8]PATTABIRAMAN K.Inverse sum indeg index of graphs[J].AKCE International Journal of Graphs and Combinatorics,2018,15:155-167.
• [9]AN M Q,XIONG L M.Some results on the inverse sum indeg index of a graph[J].Information Processing Letters,2018,134:42-46.
• [10]FATH-TABAR G H,HAMAZEH A,HOSSEIN-ZADEH S.GA2index of some graph operations[J].Filomat,2010,24(1):21-28.
• [11]SHWETHA B S,LOKESHA V,RANJINI P S.On the harmonic index of graph operations[J].Transactions on combinatorics,2015,4:5-14.
• [12]米热古丽·外力.一些图运算的调和指标与调和多项式的线图[J].新疆大学学报(自然科学版)(中英文),2021,38(5):540-548.
• [13]GUPTA C K,LOKESHA V,SHWETHA B S,et al.Graph operations on the symmetric division deg index of graphs[J].Palestine Journal of Mathematics,2017,6:280-286.
• [14]GUTMAN I,TRINAJSTIC N.Graph theory and molecular orbitals,totalπelectron energy of alternant hydrocarbons[J].Chemical Physics Letters,1972,17:535-538.
• [15]GUTMAN I,DAS K C.The first Zagreb index 30 years after[J].MATCH Communications in Mathematical and in Computer Chemistry,2004,50:83-92.
• [16]ZHOU B.Zagreb indices[J].MATCH Communications in Mathematical and in Computer Chemistry,2004,52:113-118.
• [17]DAS K C,XU K,CANGUL I N,et al.On the harary index of graph operations[J].Journal of Inequalities and Applications,2013,1:1-16.
• [18]HARARY F.Graph theory[M].Massachusetts:Addison-Wesley,1994.
• [19]KHALIFEHA M H,YOUSEFI-AZARI H,ASHRAFI A R.The hyper-wiener index of graph operations[J].Computers and Mathematics with Applications,2008,56(5):1402-1407.