2011•arXiv (Cornell University)Open access

New results on the energy of integral circulant graphs

Aleksandar Ilić, Milan Bašić

Abstract

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph $\ICG_n (D)$ has the vertex set $Z_n = \{0, 1, 2, ..., n - 1\}$ and vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in D$, where $D \subseteq \{d : d \mid n,\ 1\leq d

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Key concepts: Circulant matrix, Circulant graph, Mathematics, Combinatorics, Cayley graph, Odd graph, Integral graph, Vertex (graph theory)