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Yang, Jing; Wang, Long
Linear algebra and its applications, 11/2023, Letnik: 676Journal Article
Let T be a tree with p≥3 pendant edges and let L(T) be its line graph. In this paper, we prove the multiplicity of an arbitrary adjacency eigenvalue of L(T) is no larger than p−1. Furthermore, the line graphs L(T) of trees which contain an adjacency eigenvalue with multiplicity p−1 are completely determined.
