On the Edge-Forwarding Indices of Frobenius Graphs
نویسندگان
چکیده
A G-Frobenius graph, as defined recently 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 G. 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(Γ) 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 index of Frobenius graphs. In particular, we obtain edge-forwarding index of a G-Frobenius graph Γ with rank(G) ≤ 50 and those of Γ which has type− (n1, n2, ..., nd) where d = n, (1, 2, 3, ..., n); d = 2n− 1, (1, 2, ..., n− 1, n, n− 1, ..., 2, 1); d = 2n, (1, 2, ..., n− 1, n, n, n− 1, ...2, 1), respectively.
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