منابع مشابه
Ramanujan Graphs with Small Girth
We construct an infinite family of (q + 1)−regular Ramanujan graphs Xn of girth 1. We also give covering maps Xn+1 → Xn such that the minimal common covering of all the Xn’s is the universal covering tree.
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A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...
متن کاملSmall Regular Graphs of Girth 7
In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7...
متن کاملRamanujan Graphs
In the last two decades, the theory of Ramanujan graphs has gained prominence primarily for two reasons. First, from a practical viewpoint, these graphs resolve an extremal problem in communication network theory (see for example [2]). Second, from a more aesthetic viewpoint, they fuse diverse branches of pure mathematics, namely, number theory, representation theory and algebraic geometry. The...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2003
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-003-0029-9