关于路径和循环的广播
Broadcasts on Paths and Cycles
摘要：
图$G=(V,E)$上的广播是函数$f: V\longrightarrow \{0,\ldots,\operatorname{diam}(G)\}$，使得对于每个顶点$v\in V$，$f(v)\leq e\_G(v)$，其中$\operatorname{diam}(G)$表示$G$的直径，并且$e\_G(v)$表示$v$在$G$中的偏心率。这种广播的代价就是值$\sum\_{v\in V}f(v)$ .文献中考虑了图上各种类型的广播函数，它们与支配、无冗余、独立或填充有关，从而引入了图上的几种广播数.本文确定了所有路和圈的广播数，从而回答了[D.~]中提出的一个问题.艾哈迈迪，GH ~ C.J.~ Schroeder，S.T.~ Hedetniemi和R.C.~ Laskar，在图表中广播无冗余。{ \it符合性编号} 224（2015），17- 31]。
英文摘要：
A broadcast on a graph $G=(V,E)$ is a function $f: V\longrightarrow \{0,\ldots,\operatorname{diam}(G)\}$ such that $f(v)\leq e\_G(v)$ for every vertex $v\in V$, where$\operatorname{diam}(G)$ denotes the diameter of $G$ and $e\_G(v)$ the eccentricity of $v$ in $G$. The cost of such a broadcast is then the value $\sum\_{v\in V}f(v)$.Various types of broadcast functions on graphs have been considered in the literature, in relation with domination, irredundence, independenceor packing, leading to the introduction of several broadcast numbers on graphs.In this paper, we determine these broadcast numbers for all paths and cycles, thus answering a questionraised in [D.~Ahmadi, G.H.~Fricke, C.~Schroeder, S.T.~Hedetniemi and R.C.~Laskar, Broadcast irredundance in graphs. {\it Congr. Numer.} 224 (2015), 17--31].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
