منابع مشابه
Cubic Cayley graphs with small diameter
In this paper we apply Pólya’s Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group. We report the results of a search of all three-regular Cayley graphs on permutation groups of degree at most nine for small diameter graphs. We explore several methods of constructing covering graphs of these Cayley graphs. Exam...
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For any d ≥ 5 and k ≥ 3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((d−3)/3)k. By comparison with other available results in this area we show that, for all sufficiently large d and k, our family gives the current largest known Cayley graphs of degree d and diameter k.
متن کاملLarge bipartite Cayley graphs of given degree and diameter
Let BCd,k be the largest possible number of vertices in a bipartite Cayley graph of degree d and diameter k. We show that BCd,k ≥ 2(k−1)((d−4)/3)k−1 for any d ≥ 6 and any even k ≥ 4, and BCd,k ≥ (k − 1)((d− 2)/3)k−1 for d ≥ 6 and k ≥ 7 such that k ≡ 3 (mod 4).
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Let 5 be a subset gener<lIing a fin ite group G. The corresponding Cayley gruph '§(G , 5 ) has the e lements of G as vertices ~od the. pairs 19. $g f. g E' G. $ E S . as edges. The diameter Q( ':!}(G , 5 ) is the smallL'lll iotcger d such thai every clement of G can be expressed as a word uf leoglh .,,;;. d using c lements (rom 5 U S ". A simple counl of words shows thai d ~ 10g~ I~ 1 (IG O. We...
متن کاملThe correct diameter of trivalent Cayley graphs
Let n be a positive integer with n> 2. The trivalent Cayley interconnection network, denoted by TCIN(n), is proposed by Vadapalli and Srimani (1995). Later, Vadapalli and Srimani (1996) claimed that the diameter of TCIN(n) is 2n − 1. In this paper, we argue that the above claim is not correct. Instead, we show that the diameter of TCIN(n) is 2n− 1 only for n= 2 and 2n− 2 for all other cases. ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.04.025