Spectral properties of the exponential distance matrix
INVOLVE, A JOURNAL OF MATHEMATICS(2019)
Abstract
Given a graph $G$, the exponential distance matrix is defined entry-wise by letting the $(u,v)$-entry be $q^{\text{dist}(u,v)}$, where $\text{dist}(u,v)$ is the distance between the vertices $u$ and $v$ with the convention that if vertices are in different components, then $q^{\text{dist}(u,v)}=0$. In this paper, we will establish several properties of the characteristic polynomial (spectrum) for this matrix, give some families of graphs which are uniquely determined by their spectrum, and produce cospectral constructions.
MoreTranslated text
Key words
exponential distance matrix, spectral graph theory, Cartesian product, cospectral graphs
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined