More on Graphs with Just Three Distinct Eigenvalues
نویسنده
چکیده
Let G be a graph of order n with (0, 1)-adjacency matrix A. An eigenvalue σ of A is said to be an eigenvalue of G, and σ is a main eigenvalue if the eigenspace EA(σ) is not orthogonal to the all-1 vector in IR. Always the largest eigenvalue, or index, of G is a main eigenvalue, and it is the only main eigenvalue if and only if G is regular. We say that G is an integral graph if every eigenvalue of G is an integer; and G is a biregular graph if it has just two different degrees. We use the notation of the monograph [6], where the basic properties of graph spectra can be found in Chapter 1. Let C1 be the class of connected graphs with just three distinct eigenvalues, and let C2 be the class of connected graphs with exactly two main eigenvalues. It is an open problem to determine all the graphs in C1, and another open problem to determine all the graphs in C2. Here we continue the investigation of graphs in
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