We calculate the rank of all graphs obtained by adding two vertices to a complete graph. We give some properties of maximal reduced graphs, graphs which occur ...
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65 Citations · Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows · Minimal basis for a vector space with an application to ...
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Spectral graph theory uses eigenvalues and eigenvectors of matrices associated with the graph to study its combinatorial properties. In this chapter, we ...
Jul 8, 2011 · Here is a simple proof. Without loss of generality, G′ is obtained from G by deleting some edges (and keeping all vertices).
May 13, 2013 · Spectral graph theory concerns the connection and interplay between the subjects of graph theory and linear algebra.
The spectrum of a graph G is the set of eigenvalues of A(G) together with their multiplicities. Since A (short for A(G)) is a real symmetric matrix, basic ...
Mar 8, 2011 · Let G be a graph and H a subgraph of G. In this paper, a set of pairwise independent subgraphs that are all isomorphic copies of H is called.
Mar 18, 2020 · Let G be a graph with adjacency matrix AG and H be an induced subgraph of G. Let H∗ be a graph with same number of vertices as ...
Graph spectrum. This chapter presents some simple results on graph spectra. We assume the reader to be familiar with elementary linear algebra and graph theory.
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