The domination number of G is the size of its smallest dominating set(s). In this paper we give an upper bound on the number of edges a connected graph with a given number of vertices and a given domination number can have. We also characterize the extremal graphs attaining this upper ...
2. Proof of Theorem 3 We want to derive a linear in (n−k) bound on the number of edges in a graph that does not contain (k+1)-connected subgraphs. But the bound becomes linear only for graphs with large number of vertices; while for small graphs the dependency is quadratic in n...
摘要: We prove that the maximal number of directed edges in a vertex-critical strongly connected simple digraph on n vertices is n(n-1)/2 - n +4.关键词: strongly connected digraphs vertex-critical DOI: 10.1016/S0012-365X(00)00395-2 被引量: 9 ...
MinCostFlowReinelt<int> mcf;// construct min-cost flow problemGraphCopy GC; GC.createEmpty(G);// compute connected component of GNodeArray<int> component(G);intnumCC = connectedComponents(G,component);// intialize the array of lists of nodes contained in a CCArray<List<node> > nodesInCC...
A LOWER BOUND FOR THE NUMBER OFEDGES IN A GRAPH CONTAINING NO TWOCYCLES OF THE SAME LENGTHChunhui Lai∗Dept. of Math., Zhangzhou Teachers College,Zhangzhou, Fujian 363000, P. R. of CHINA.zjlaichu@public. zzptt. fj. cnSubmitted: November 3, 2000; Accepted: October 20, 2001.MR ...
Bounds on the Steiner radius of a graph For a connected graph G of order p and a set SV(G), the Steiner distance of S is the minimum number of edges in a connected subgraph of G containing S. If ... A Patrick,BE Tri - 《Discrete Mathematics Algorithms & Applications》 被引量: 0...
For an ed ge e of G; we do the following operations on G: first, delete the edge e from G; resulting the graph Ge; second, for all the vertices x of degree 3i nGe; delete x from Ge andthen completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we ...
issaidto beadjacentto ΦinΓ.IfZIis asubgraphof thegraphΓthenanyvertexofAincident withanedgeof$(Γ)—$(A)iscalledadasp-vertexofΔinΓ.If F is avertexof thegraphΓthenthenumberofedgesofJTincident withF iscalledthevalencyofVίηΓanddenotedbyv(F,Γ).Apathis agraph consistingofndistinct...
Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to find the number of connected components in an undirected graph. Example 1: 0 3 | | 1 --- 2 4 Given n = 5 and edges = [[0, 1], [1, 2], [3, ...
You have a graph ofnnodes. You are given an integernand an arrayedgeswhereedges[i] = [ai, bi]indicates that there is an edge betweenaiandbiin the graph. Returnthe number of connected components in the graph. Example 1: Input: n = 5, edges = [[0,1],[1,2],[3,4]] ...