Strongly self-dual graphs |
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Authors: | RM Tifenbach |
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Institution: | Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland |
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Abstract: | We present a class of graphs whose adjacency matrices are nonsingular with integral inverses, denoted h-graphs. If the h-graphs G and H with adjacency matrices M(G) and M(H) satisfy M(G)-1=SM(H)S, where S is a signature matrix, we refer to H as the dual of G. The dual is a type of graph inverse. If the h-graph G is isomorphic to its dual via a particular isomorphism, we refer to G as strongly self-dual. We investigate the structural and spectral properties of strongly self-dual graphs, with a particular emphasis on identifying when such a graph has 1 as an eigenvalue. |
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Keywords: | 05C50 15A09 |
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