Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have