On quasi-strongly regular graphs |
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Authors: | Felix Goldberg |
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Institution: |
a Department of Mathematics, Technion-IIT, Haifa, Israel |
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Abstract: | We study the quasi-strongly regular graphs, which are a combinatorial generalization of the strongly regular and the distance regular graphs. Our main focus is on quasi-strongly regular graphs of grade 2. We prove a “spectral gap”-type result for them which generalizes Seidel's well-known formula for the eigenvalues of a strongly regular graph. We also obtain a number of necessary conditions for the feasibility of parameter sets and some structural results. We propose the heuristic principle that the quasi-strongly regular graphs can be viewed as a “lower-order approximation” to the distance regular graphs. This idea is illustrated by extending a known result from the distance-regular case to the quasi-strongly regular case. Along these lines, we propose a number of conjectures and open problems. Finally, we list the all the proper connected quasi-strongly graphs of grade 2 with up to 12 vertices. |
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Keywords: | AMS Subject Classifications: 05E30 05C50 15A42 |
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