Horizontal visibility graphs from integer sequences

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چکیده

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Integer sequences from walks in graphs

We define numbers of the type Oj(N) = N – N + N – ... + N and E(N) = –N + N – N + ... + N (j = 0, 1, 2, ...) and the corresponding integer sequences. We prove that these integer sequences, e.g., S0(N) = O0(N), O1(N), ..., Or(N), ... and SE(N) = E0(N), E1(N), ..., Er(N), ... correspond to the number of odd and even walks in complete graphs KN. We then prove that there is a unique family of graph...

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ژورنال

عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical

سال: 2016

ISSN: 1751-8113,1751-8121

DOI: 10.1088/1751-8113/49/35/35lt01