Spectra of graphs: theory and application
The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. However, that does not mean that the theory of graph spectra can be reduced to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.
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Basic Properties of the Spectrum of a Graph
Operations on Graphs and the Resulting Spectra
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A. J. Hoffman According to Theorem adjacency matrix automorphism group basic figure bipartite graph characteristic polynomial characterized chromatic number circuit of length coefficients complete bipartite graph complete graph components connected graph considered corresponding cospectral graphs cubic graphs Cve9 cycles D. M. Cvetkovic defined denote determined digraph direct sum distinct eigenvalues eigenvalues of G eigenvector equal equation equiangular lines exactly finite following theorem front divisor G contains G is regular given graph G graph of degree graph spectra graph theory Hence induced subgraph inequality integer isomorphic J. J. Seidel Lemma Let G line graph Math molecular orbitals Moore graphs multi-(di-)graph multi-digraph multigraph multiplicity NEPS non-adjacent non-negative number of vertices number of walks obtained p-sum pair parameters permutation problem properties proved relation respectively Section spectrum of G strongly regular graphs symmetric Theorem trees two-graph undirected valency vector vertices of G walks of length zero