An Eigenvalue Characterization of Antipodal Distance-Regular Graphs
Copyright policy )An Eigenvalue Characterization of Antipodal Distance-Regular Graphs
Let $G$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $G$ is an $r$-antipodal distance-regular graph if and only if the distance graph $G_d$ is constituted by disjoint copies of the complete graph $K_r$, with $r$ satisfying an expression in terms of $n$ and the distinct eigenvalues.
Teoria de, Graphs and linear algebra (matrices, eigenvalues, etc.), Grafs, Teoria de, Alternating polynomials, Classificació AMS::05 Combinatorics::05C Graph theory, Eigenvalues, Graph theory, Grafs, Antipodal distance-regular graph, Combinacions (Matemàtica), Combinatorics, Association schemes, strongly regular graphs, :05 Combinatorics::05E Algebraic combinatorics [Classificació AMS], :05 Combinatorics::05C Graph theory [Classificació AMS], Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Teoria de, Graphs and linear algebra (matrices, eigenvalues, etc.), Grafs, Teoria de, Alternating polynomials, Classificació AMS::05 Combinatorics::05C Graph theory, Eigenvalues, Graph theory, Grafs, Antipodal distance-regular graph, Combinacions (Matemàtica), Combinatorics, Association schemes, strongly regular graphs, :05 Combinatorics::05E Algebraic combinatorics [Classificació AMS], :05 Combinatorics::05C Graph theory [Classificació AMS], Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
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