The Generating graph of Dicyclic Groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914339231891456 |
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| author | Samant, Kavita Reddy, A. Satyanarayana |
| author_facet | Samant, Kavita Reddy, A. Satyanarayana |
| contents | For a group $G,$ the generating graph of $G,$ denoted by $Γ(G).$ We define $Q_n=\langle x,y: x^{2n}=y^4=1, x^n=y^2,y^{-1}xy=x^{-1}\rangle,$ the dicyclic group of order $4n.$ This paper primarily delves into exploring the graph characteristics and spectral properties of various matrices associated with $Γ(Q_n)$. Specifically, we determine the complete spectrum of the adjacency, Laplacian, distance, and eccentricity matrices. Additionally, we completely determine the spectrum pertaining to the distance and eccentricity matrices of the dihedral group of order $2n$, denoted as $D_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_05157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Generating graph of Dicyclic Groups Samant, Kavita Reddy, A. Satyanarayana Combinatorics 05C25, 05C50, 20D60 For a group $G,$ the generating graph of $G,$ denoted by $Γ(G).$ We define $Q_n=\langle x,y: x^{2n}=y^4=1, x^n=y^2,y^{-1}xy=x^{-1}\rangle,$ the dicyclic group of order $4n.$ This paper primarily delves into exploring the graph characteristics and spectral properties of various matrices associated with $Γ(Q_n)$. Specifically, we determine the complete spectrum of the adjacency, Laplacian, distance, and eccentricity matrices. Additionally, we completely determine the spectrum pertaining to the distance and eccentricity matrices of the dihedral group of order $2n$, denoted as $D_n$. |
| title | The Generating graph of Dicyclic Groups |
| topic | Combinatorics 05C25, 05C50, 20D60 |
| url | https://arxiv.org/abs/2406.05157 |