Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599984 | Linear Algebra and its Applications | 2013 | 8 Pages |
Abstract
A threshold graph on n vertices is coded by a binary string of length nâ1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph in terms of the code of the graph. It is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the number of ones in the code, whereas the nullity is given by the number of zeros in the code that are preceded by either a zero or a blank. A formula for the determinant of the adjacency matrix of a generalized threshold graph and the inverse, when it exists, of the adjacency matrix of a threshold graph are obtained. Results for antiregular graphs follow as special cases.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
R.B. Bapat,