A minimum broadcast graph on 63 vertices
نویسنده
چکیده
We describe the construction of a minimum broadcast graph with 63 vertices. The graph has 162 edges.
منابع مشابه
Girth, minimum degree, independence, and broadcast independence
An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...
متن کاملA minimum broadcast graph on 26 vertices
Broadcasting is the process of information dissemination in a communication network in which a message, originated by one member, is transmitted to all members of the network. A broadcast graph is a graph which permits broadcasting from any originator in minimum time. The broadcast function B(n) is the minimum number of edges in any broadcast graph on n vertices. In this paper, we construct a b...
متن کاملBroadcasting from multiple originators
We begin an investigation of broadcasting from multiple originators, a variant of broadcasting in which any k vertices may be the originators of a message in a network of n vertices. The requirement is that the message be distributed to all n vertices in minimum time. A minimum k-originator broadcast graph is a graph on n vertices with the fewest edges such that any subset of k vertices can bro...
متن کاملBroadcasting in planar graphs
For an arbitrary graph on n vertices, the minimum time required to broadcast is pogz n 1, and for any n, there exist graphs on n vertices with broadcast time equal to fIogz n 1. When restricted to planar graphs, this is generally not the case; however, just one additional time unit is sufficient to allow broadcasting in certain planar graphs. We also show that the maximum number of vertices in ...
متن کاملEfficient construction of broadcast graphs
A broadcast graph is a connected graph, G = (V,E), |V | = n, in which each vertex can complete broadcasting of one message within at most t = ⌈logn⌉ time units. A minimum broadcast graph on n vertices is a broadcast graph with the minimum number of edges over all broadcast graphs on n vertices. The cardinality of the edge set of such a graph is denoted by B(n). In this paper we construct a new ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 53 شماره
صفحات -
تاریخ انتشار 1994