The Weisfeiler-Leman Dimension of Distance-Hereditary Graphs

被引：2
|
作者：
Gavrilyuk, Alexander L. [1 ]
Nedela, Roman [2 ]
Ponomarenko, Ilia [3 ,4 ]
机构：
[1] Shimane Univ, Matsue, Japan
[2] Univ West Bohemia, Dept Math, Plzen, Czech Republic
[3] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China
[4] St Petersburg Dept Steklov Math Inst, St Petersburg, Russia
来源：
GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 04期
关键词：
Distance-hereditary graph; Weisfeiler-Leman algorithm; Weisfeiler-Leman dimension; Graph isomorphism;
D O I：
10.1007/s00373-023-02683-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove that the ordinary Weisfeiler-Leman algorithm tests the isomorphism of any two graphs if one of them is distance-hereditary; more precisely, the Weisfeiler-Leman dimension of the class of finite distance-hereditary graphs is equal to 2. The previously best known upper bound for the dimension was 7.
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页数：19
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