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Broadcasting in Optimal Bipartite Double Loop Graphs

机译:广播在最佳的双链双环图中

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Double loop graphs are extensions of the ring topology which are obtained by regularly adding 2 extra edges per vertex. An optimal graph of diameter d has the maximum possible number of vertices. The optimal structure of double loop graphs, as well as the broadcast time and an optimal broadcast scheme are known. In this paper, we define the family of bipartite double loop graphs (BDLG) G = (V,E) where V = V_0 u V_1, V_0 n V_1 = f and |V0| = |V1|. We show that the maximum number of vertices that a BDLG of diameter d can have is 2d2. We also study the broadcast problem and find that the broadcast time is d + 2. Finally we present an optimal broadcast scheme for these bipartite double loop graphs.
机译:双环图是环形拓扑的延伸,通过定期添加每个顶点2额外的边缘而获得。直径D的最佳图D具有最大可能数量的顶点。已知双环图的最佳结构以及广播时间和最佳广播方案。在本文中,我们定义了二分的双环图(BDLG)G =(v,e)的系列,其中v = v_0uv_1,v_0 n v_1 = f和| v0 | = | v1 |。我们表明,直径D的BDLG可以具有的最大顶点数是2D2。我们还研究了广播问题,发现广播时间为D + 2.最后我们为这些二分的双环图提供了最佳广播方案。

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