A construction of cospectral signed line graphs

	A construction of cospectral signed line graphs
Communications in Combinatorics and Optimization
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 10 دی 1403 اصل مقاله (383.25 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2024.30034.2284
نویسنده
Zoran Stanić^*
Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000 Belgrade, Serbia
چکیده
For an ordinary graph $G$, we compute the eigenvalues and the eigenspaces of the signed line graph $\mathcal{L}(\ddot{G})$, where $\ddot{G}$ is obtained from $G$ by inserting a negative parallel edge between every pair of adjacent vertices. As an application, we prove that if $G$ and $H$ share the same vertex degrees, then $\mathcal{L}(\ddot{G})$ and $\mathcal{L}(\ddot{H})$ share the same spectrum. To the best of our knowledge, this construction does not follow the line of any known construction developed for either graphs or signed graphs. Among the other consequences, we emphasize that $\mathcal{L}(\ddot{G})$ is integral (i.e., its spectrum consists entirely of integers), which means that a construction of integral signed graphs has been established simultaneously.
کلیدواژه‌ها
Vertex degree؛ Signed line graph؛ Adjacency matrix؛ Eigenspace؛ Integral spectrum

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