论文标题
统治广播：关于周期图和阳光图组合的案例研究
Domination broadcast: A case study on a combination of cycle graph and sunlet graph
论文作者
论文摘要
长期以来一直研究了图中的统治，并应用于信号分布问题。例如，电信公司希望通过向所有接收站传输不同的信号强度，从广播电台传播信号。这个问题可以用图理论的术语来解释。假设广播公司需要使用具有不同信号强度的广播电台将信号传播到图中，以便可以将信号发送到所有顶点。但是，信号更强的广播电台通常更昂贵。信号的分布被配置为覆盖所有信号总成本，称为$γ_b-$主导广播号码。本文展示了$γ_b-$主导广播数的另一个周期图和太阳图图的另一个证明，以此作为进一步结果的基础。我还考虑$γ_b-$统治广告的阳光图的广播号码，其周期上的顶点同样由路径扩展，称为$ n $ $ n $的Sunlet Graph。为了获得此扩展版本的信号分布的最佳成本，我们表明，在周期上仅使用一个顶点的一个广播站，信号成本等于$ n $的信号成本等于Sunlet Graph的半径。
Domination in graphs has long been studied and is applied to signal distribution problem. For example, telecommunication companies want to spread the signal from broadcast stations by transmitting varying signal strength to all receiving stations. This problem can be interpreted in a term of graph theory. Assume that broadcast companies need to spread the signal in graphs by using broadcast stations with varying signal strength so that the signal could be sent to all the vertices. However, broadcast stations with stronger signal are generally more expensive. The distribution of signal was configured to cover all stations with minimum total cost of signal called the $γ_b-$dominating broadcast number. This paper shows another proof of the $γ_b-$dominating broadcast number of cycle graphs and sunlet graphs as a foundation for the further result. I also consider the $γ_b-$dominating broadcast number of a generalized version of sunlet graphs whose vertices on the cycle are equally extended by the path, called the sunlet graph with degree $n$. To obtain the optimal cost of the signal distribution for this extended version, we show that it is sufficient to use only one broadcast station at a vertex on the cycle with the signal cost equal to the radius of the sunlet graph with degree $n$.
