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On the Energy of the line graph of Unitary Cayley graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 تیر 1403 اصل مقاله (344.38 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29624.2091 | ||
| نویسنده | ||
| Fateme Movahedi* | ||
| Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran | ||
| چکیده | ||
| The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of the line graph of graph $G$ is denoted by $E(L(G))$. The unitary Cayley graph $X_n$ is a graph with the vertex set $Z_n=\{0, 1, \ldots, n-1\}$ and the edge set $\{(a,b) \, : \, ged(a-b,n)=1\}$. In this paper, we focus on the line graph of the unitary Cayley graph $X_n$ and compute the spectrum of line graphs of $X_n$ and its complement graph $\overline{X_n}$. We also obtain the energy of the line graph of $X_n$ and $\overline{X_n}$. | ||
| کلیدواژه‌ها | ||
| Graph energy؛ Unitary Cayley graph؛ Spectrum؛ Complement؛ Line graph | ||
| مراجع | ||
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[14] F. Movahedi, The energy and edge energy of some Cayley graphs on the abelian group $\mathbb{Z}_n^4$, Commun. Comb. Optim. 9 (2024), no. 1, 119–130. https://doi.org/10.22049/cco.2023.28642.1647 [15] N. Palanivel and A.V. Chithra, Energy and Laplacian energy of unitary addition Cayley graphs, Filomat 33 (2019), no. 11, 3599–3613. https://doi.org/10.2298/FIL1911599P [16] H.N. Ramaswamy and C.R. Veena, On the energy of unitary Cayley graphs, Electron. J. Comb. 16 (2009), no. 1, Article Number: N24 https://doi.org/10.37236/262 | ||
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