This article is cited in 2 papers

Applied Graph Theory

A set of families of analytically described triple loop networks defined by a parameter

E. A. Monakhova

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

Abstract: A set of families of undirected triple loop networks of the form $C(N(d,p); 1, s_2(d,p),$ $ s_3(d,p))$ with the given diameter $d>1$ and a parameter $p=1, 2, \ldots, d-1$ is obtained. For each such family, the order $N$ of every graph in the family and its generators $s_2$ and $s_3$ are defined by a cubical polynomial function of the diameter. The found set includes circulant graphs of degree 6 with the largest known orders for any diameters $d\equiv 0 \pmod 3$ and $d\equiv 2 \pmod 3$. Examples of constructing new families of triple loop networks based on the definition of functions $p=p(d)$ are presented.

Keywords: undirected triple loop networks, circulant graphs of degree $6$ with given diameter, families of circulant graphs.

UDC: 519.87

DOI: 10.17223/20710410/49/8

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