A construction of cospectral signed line graphs

Articles in Press

Document Type : Original paper

Author

Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000 Belgrade, Serbia

Abstract

For an ordinary graph G, we compute the eigenvalues and the eigenspaces of the signed line graph L(G¨), where 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 L(G¨) and L(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 L(G¨) is integral (i.e., its spectrum consists entirely of integers), which means that a construction of integral signed graphs has been established simultaneously.

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Main Subjects

Communications in Combinatorics and Optimization

Articles in Press, Corrected Proof
Available Online from 30 December 2024

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