Asymptotic aspects of Cayley graphs
نویسنده
چکیده
Arising from complete Cayley graphs Γn of odd cyclic groups Zn, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equallymulticolored copies of K4 in Γn with adjacency of any two such vertices whenever they are represented by copies of K4 in Γn sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order |V |1/3, properties shared by the initial member of a collection of families of Cayley graphs of degree 2m ≥ 6 with diameter asymptotically of order |V |1/m, where 3 ≤ m ∈ Z.
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