On the inverse graph of a finite group and its rainbow connection number
| Main Authors: | Umbara, Rian Febrian; 1. Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. 2. School of Computing, Telkom University, Jl. Telekomunikasi Terusan Buah Batu, Bandung, 40257, Jawa Barat, Indonesia, Salman, A.N.M.; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Putri, Pritta Etriana; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1681 https://www.ejgta.org/index.php/ejgta/article/view/1681/pdf_259 https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/1681/308 |
Daftar Isi:
- A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called the rainbow connection number of G. Let (Γ, *) be a finite group with TΓ = {t ∈ Γ|t ≠ t−1}. The inverse graph of Γ, denoted by IG(Γ), is a graph whose vertex set is Γ and two distinct vertices, u and v, are adjacent if u * v ∈ TΓ or v * u ∈ TΓ. In this paper, we determine the necessary and sufficient conditions for the inverse graph of a finite group to be connected. We show that the inverse graph of a finite group is connected if and only if the group has a set of generators whose all elements are non-self-invertible. We also determine the rainbow connection numbers of the inverse graphs of finite groups.