Generating Graphs of Finite Dihedral Groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913655023468544 |
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| author | Reddy, A. Satyanarayana Samant, Kavita |
| author_facet | Reddy, A. Satyanarayana Samant, Kavita |
| contents | For a group $G$, the generating graph $Γ(G)$ is defined as the graph with the vertex set $G$, and any two distinct vertices of $Γ(G)$ are adjacent if they generate $G$. In this paper, we study the generating graph of $D_n,$ where $D_n$ is a Dihedral group of order $2n$. We explore various graph theoretic properties, and determine complete spectrum of the adjacency and the Laplacian matrix of $Γ(D_n)$. Moreover, we compute some distance and degree based topological indices of $Γ(D_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11802 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generating Graphs of Finite Dihedral Groups Reddy, A. Satyanarayana Samant, Kavita Combinatorics Group Theory 05C25, 05C50, 20D60 For a group $G$, the generating graph $Γ(G)$ is defined as the graph with the vertex set $G$, and any two distinct vertices of $Γ(G)$ are adjacent if they generate $G$. In this paper, we study the generating graph of $D_n,$ where $D_n$ is a Dihedral group of order $2n$. We explore various graph theoretic properties, and determine complete spectrum of the adjacency and the Laplacian matrix of $Γ(D_n)$. Moreover, we compute some distance and degree based topological indices of $Γ(D_n)$. |
| title | Generating Graphs of Finite Dihedral Groups |
| topic | Combinatorics Group Theory 05C25, 05C50, 20D60 |
| url | https://arxiv.org/abs/2307.11802 |