We discuss the minimal number of vertices in a graph with a large chromaticnumber such that each ball of a fixed radius in it has a small chromaticnumber. It is shown that for every graph $G$ on $\\sim((n+rc)/(c+rc))^{r+1}$vertices such that each ball of radius $r$ is ...
2. Show that a graph has an even number of vertices of odd degree. 相关知识点: 试题来源: 解析 If we add all the degrees of all the vertices, then we must obtain twice the number of edges,since each edge joins two vertices. Hence the sum of all degrees of all vertices is even. ...
作者: Goddard, Wayne,Henning, Michael A,McPillan, Charles A 摘要: For a positive integer b, we define a set S of vertices in a graph G as a b-disjunctive dominating set if every vertex not in S is adjacent to a vertex of S or has at least b vertices in S at distance 2 from...
Domatic number and degrees of vertices of a graph 来自 Semantic Scholar 喜欢 0 阅读量: 57 作者: B Zelinka 摘要: In [3] the interconnections between the domatic number of a graph and the degrees of its vertices were studied. Here we shall transfer those results to the total domatic ...
For v∈V(G), ≔N(v)≔{u∈V(G):uv∈E(G)} denotes the neighborhood of v in G. Let k∈N. Recall that a graph G is (k+1)-connected if, for every set S⊂V(G) of size k, the graph G[V(G)∖S] is connected and contains at least two vertices (so |V(G)|≥k+...
[cs.CC] 5 Feb 2016A Note on the Complexity of Computing theNumber of Reachable Vertices in a DigraphMichele BorassiMarch 26, 2018AbstractIn this work, we consider the following problem: given a digraph G =(V,E), for each vertex v, we want to compute the number of verticesreachable ...
In this section, we’ll present a general formula to calculate the maximum number of edges that a directed graph can contain. Let’s assume an undirected graph with vertices. Further, we’re also assuming that the graph has a maximum number of edges. In such a case, from the starting v...
On this paper, we fix the number of cliques that cover a graph by the same number of vertices that the graph has, and give an upper bound for the sum of the number of vertices of these cliques in the cases where this covering is possible. 关键词: Mathematics - Combinatorics DOI: ...
For a graph G and k a real number, we consider the sum of the kth powers of the degrees of the vertices of G. We present some general bounds on this sum fo... SM Cioaba - 《Discrete Mathematics》 被引量: 75发表: 2008年 On the Cover Time for Random Walks on Random Graphs The ...
结果1 题目 Let G be a connected planar graph. If v is the number of vertices, e is the number of edges and f is the number of faces and v=e, then f=___.A、2B、2e-2 相关知识点: 试题来源: 解析 A 反馈 收藏