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From Integer Sequences to Block Designs via Counting Walks in Graphs | | Ernesto Estrada
; José A. de la Peña
; | | Date: |
5 Feb 2013 | | Abstract: | We define numbers of the type Oj(N) and Ej(N) and the corresponding integer
sequences. We prove that these integer sequences, e.g., SO(N) and SE(N)
correspond to the number of odd and even walks in complete graphs. We then
prove that there is a unique family of graphs which have exactly the same
sequence of odd walks between connected nodes and of even walks between pairs
of nodes at distance two, respectively. These graphs are obtained as the
Kronecker product. We show that they are the incidence graphs of block designs,
are distance-regular and Ramanujan graphs. | | Source: | arXiv, 1302.1176 | | Services: | Forum | Review | PDF | Favorites | |
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