On the Edge-forwarding Indices of Frobenius Graphs

AbstractA G-Frobenius graph Γ, as defined by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group G = K ⋊ H with Frobenius kernel K and Frobenius complement H. Γ is also shown to be a Cayley graph, Γ = Cay(K, S) for K and some subset S of the group K. On the other hand, a network N with a routing function R, written as (N,R), is an undirected graph N together with a routing R which consists of a collection of simple paths connecting every pair of vertices in the graph. The edge-forwarding index π(N) of a network (N,R), defined by Heydemann, Meyer, and Sotteau, is a parameter to describe the maximum load of edges of N. In this paper, we study the edge-forwarding indices of Frobenius graphs. In particular, we obtain the edge-forwarding index of a G-Frobenius graph Γ with rank(G) ≤ 50.

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