Maximum number of subtrees in cacti and block graphs

被引:4
|
作者
Li, Jie [1 ,2 ]
Xu, Kexiang [1 ,2 ]
Zhang, Tianli [1 ,2 ]
Wang, Hua [3 ]
Wagner, Stephan [4 ,5 ]
机构
[1] Nanjing Univ Aeronaut & Astronaut, Coll Math, Nanjing 210016, Peoples R China
[2] Comp Air Vehicles, MIIT Key Lab Math Modelling & High Performance, Nanjing 210016, Peoples R China
[3] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA
[4] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
[5] Stellenbosch Univ, Dept Math Sci, ZA-7602 Stellenbosch, South Africa
关键词
Number of subtrees; Cactus graph; Block graph; WIENER INDEX; TREES;
D O I
10.1007/s00010-022-00879-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For a graph G, we denote by N(G) the number of non-empty subtrees of G. As a topological index based on counting, N(G) has some correlations to other well studied topological indices, including the Wiener index W(G). In this paper we characterize the extremal graphs with the maximum number of subtrees among all cacti of order n with k cycles. Similarly, the extremal graphs with the maximum number of subtrees among all block graphs of order n with k blocks are also determined and shown to have the minimum Wiener index within the same collection of graphs. Analogous results are also obtained for the number of connected subgraphs C(G). Finally, a general question is posed concerning the relation between the number of subtrees and the Wiener index of graphs.
引用
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页码:1027 / 1040
页数:14
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