On graphs whose smallest distance (signless Laplacian) eigenvalue has large multiplicity
- 16 October 2017
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 66 (11) , 2218-2231
Abstract
Denote by (resp. ) the distance (resp. distance signless Laplacian) eigenvalues of a connected graph G on n vertices, and by (resp. ) the multiplicity of (resp. ). In this paper, we completely determine the graphs with and , respectively.Keywords
Funding Information
- National Natural Science Foundation of China (11531011,11671344)
This publication has 17 references indexed in Scilit:
- Distance spectra of graphs: A surveyLinear Algebra and its Applications, 2014
- The graphs with all but two eigenvalues equal to $\pm 1$ ± 1Journal of Algebraic Combinatorics, 2014
- Two Laplacians for the distance matrix of a graphLinear Algebra and its Applications, 2013
- A Nonregular Analogue of Conference GraphsJournal of Combinatorial Theory, Series A, 1999
- Nonregular Graphs with Three EigenvaluesJournal of Combinatorial Theory, Series B, 1998
- Small regular graphs with four eigenvaluesDiscrete Mathematics, 1998
- On graphs with three eigenvaluesDiscrete Mathematics, 1998
- Regular graphs with four eigenvaluesLinear Algebra and its Applications, 1995
- Multiplicative cones — a family of three eigenvalue graphsAequationes mathematicae, 1981
- Complement reducible graphsDiscrete Applied Mathematics, 1981