Bibliographic Details
| Title: |
Notes on the Equitable Graph of Type I of a Group. |
| Authors: |
Ma, Xuanlong1 xuanlma@xsyu.edu.cn, Zhang, Bin2 zhangbata@126.com, Zhai, Liangliang1 zhailiang111@126.com, Pan, Junyao3 junyaopan@126.com |
| Source: |
IAENG International Journal of Applied Mathematics. Apr2026, Vol. 56 Issue 4, p1242-1247. 6p. |
| Subjects: |
Finite groups, Planar graphs, Graph theory, Group theory, Graph connectivity |
| Abstract: |
Given a finite group G, the equitable graph of type I of G is a simple graph whose vertex set is G, in which distinct a, b ∈ G are adjacent whenever |o(a)-o(b)| ≤ min{o(a), o(b)}, where o(a) and o(b) are the orders of a and b, respectively. In this paper, we discuss some properties of the equitable graph of type I of a finite group. More specifically, we first obtain a few necessary and sufficient conditions for an equitable graphs of type I to be connected. Then, we classify all finite groups whose equitable graph of type I is planar. Finally, we give a complete classification for toroidal equitable graphs of type I. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
