Various spectral aspects of NCCC-graphs of certain finite non-abelian groups
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866911124971061248 |
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| author | Chakraborty, Rishabh Jannat, Firdous Ee Nath, Rajat Kanti |
| author_facet | Chakraborty, Rishabh Jannat, Firdous Ee Nath, Rajat Kanti |
| contents | Let ${G}$ be a finite non-abelian group. The non-commuting conjugacy class graph (abbreviated as NCCC-graph) of $G$ is a simple undirected graph whose vertex set is the set of conjugacy classes of non-central elements of $G$ and two vertices $x^G$ and $y^G$ are adjacent to each other if $x'$ and $y'$ does not commute for all $x'\in x^G$ and $y'\in y^G$, where $x^G$ is the conjugacy class of $x \in G$. In this paper, we compute the spectrum, Laplacian spectrum, signless Laplacian spectrum and corresponding energies of NCCC-graphs of certain families of finite non-abelian groups. We determine whether these graphs are integral, L-integral and Q-integral. Further, we compare energy, Laplacian energy and signless Laplacian energy; and determine whether these graphs are borderenergetic, L-borderenergetic, Q-borderenergetic, hyperenergetic, L-hyperenergetic or Q-hyperenergetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Various spectral aspects of NCCC-graphs of certain finite non-abelian groups Chakraborty, Rishabh Jannat, Firdous Ee Nath, Rajat Kanti Combinatorics Group Theory Let ${G}$ be a finite non-abelian group. The non-commuting conjugacy class graph (abbreviated as NCCC-graph) of $G$ is a simple undirected graph whose vertex set is the set of conjugacy classes of non-central elements of $G$ and two vertices $x^G$ and $y^G$ are adjacent to each other if $x'$ and $y'$ does not commute for all $x'\in x^G$ and $y'\in y^G$, where $x^G$ is the conjugacy class of $x \in G$. In this paper, we compute the spectrum, Laplacian spectrum, signless Laplacian spectrum and corresponding energies of NCCC-graphs of certain families of finite non-abelian groups. We determine whether these graphs are integral, L-integral and Q-integral. Further, we compare energy, Laplacian energy and signless Laplacian energy; and determine whether these graphs are borderenergetic, L-borderenergetic, Q-borderenergetic, hyperenergetic, L-hyperenergetic or Q-hyperenergetic. |
| title | Various spectral aspects of NCCC-graphs of certain finite non-abelian groups |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2508.19616 |