## DIMACS TR: 2002-30

## On the Edge-Forwarding Indices of Frobenius Graphs

### Authors: Yan Wang, Xin Gui Fang, and D. Frank Hsu

**
ABSTRACT
**

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 $H$.
$\Gamma$ is also shown to be a Cayley graph, $\Gamma=Cay(K,S)$ 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 $\pi(\Gamma)$ 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 $\Gamma$ with rank$(G)\leq 50$ and those of $\Gamma$ which
has $type-(n_1,n_2,...,n_d)$ 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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