给定点数,最小度和条件直径的图的边数的上界On Size, Order, Minimum Degree and Conditional Diameter of Graphs
马花萍,田应智
摘要(Abstract)：
图G的直径是G中任意两个点之间的最大距离.给定两个正整数l和s,条件直径D(G;l,s)是点数分别为l和s的两个点集之间的最大距离.当l=s=1时,图G的条件直径D(G;1,1)恰好是图G的直径D(G).本文得到了在给定点数,最小度和条件直径下图G的边数上界,且验证了这个边数的上界是渐进紧的.
关键词(KeyWords)： 直径;条件直径;最小度
基金项目(Foundation): 国家自然科学基金(11861066;11531011);; 新疆天山青年项目(2018Q066)~~
作者(Author): 马花萍,田应智
DOI: 10.13568/j.cnki.651094.651316.2020.04.16.0005
参考文献(References)：
- [1]BONDY J A,MURTY U S R.Graph theory[M].Berlin:Springer,Graduate Texts in Mathematics 244,2008.
- [2]BALBUENA C,CARMONA A,F`ABREGA J,et al.On the connectivity and the conditional diameter of graphs and digraphs[J].Networks,1996,28:97-105.
- [3]BALBUENA C,GARC′IA-V′AZQUEZ P,MARCOTE X,et al.Conditional diameter saturated graphs[J].Networks,2008,52(4):196-201.
- [4]ERD"OS P,R′ENYI A.On a problem in the theory of graphs[J].Publ Math Inst Hungar Acad Sci,Ser B,1963,7:623-639.
- [5]ERD"OS P,R′ENYI A,S′OS V T.On a problem of graph theory[J].Studia Sci Math Hungar,1966,1:215-235.
- [6]BOLLOB′AS B.Graphs with given diameter and minimal degree[J].Ars Combin,1976,2:3-9.
- [7]ORE O.Diameters in graphs[J].J Combin Theory,1968,5:75-81.
- [8]MUKWEMBI S.On size,order,diameter and minimum degree[J].Indian J Pure Appl Math,2013,44(4):467-472.
- [9]ALI P,MAZORODZE J P,MUKWEMBI S,et al.On size,order,diameter and edge-connectivity of graphs[J].Acta Math Hungar,2017,152(1):11-24.