Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598479 | Linear Algebra and its Applications | 2016 | 5 Pages |
Abstract
Let G be a simple graph. A pendant path of G is a path such that one of its end vertices has degree 1, the other end has degree ≥3, and all the internal vertices have degree 2. Let pk(G)pk(G) be the number of pendant paths of length k of G , and qk(G)qk(G) be the number of vertices with degree ≥3 which are an end vertex of some pendant paths of length k. Motivated by the problem of characterizing dendritic trees, N. Saito and E. Woei conjectured that any graph G has some Laplacian eigenvalue with multiplicity at least pk(G)−qk(G)pk(G)−qk(G). We prove a more general result for both Laplacian and signless Laplacian eigenvalues from which the conjecture follows.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ebrahim Ghorbani,