Calculate the average number of edges in a graphElizabeth Whalen
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−k. The main difficult...
Example:G = graph(1,2) Example:G = digraph([1 2],[2 3]) Output Arguments collapse all Number of edges, returned as a scalar. Extended Capabilities expand all C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. ...
We consider the following question: what is the maximum number of edges in a K5-minor-free graph with n vertices and girth g, where n≥4? With no restriction on the girth (g=3), it is well known that the answer is 3n−6. For g=4 and n≥5, the answer is known to be 3n...
Firstly, there should be at most one edge from a specific vertex to another vertex. This ensures all the vertices are connected and hence the graph contains the maximum number of edges. In short, a directed graph needs to be a complete graph in order to contain the maximum number of edges...
Let G be a bipartite graph without loops and multiple edges on v ≥4 vertices, which can be drawn on a plane in such a way that any edge intersects at most one other edge. It is proved that such a graph has at most 3 v - 8 edges for even v ≠6 and at most 3 v - 9 ...
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 ...
We obtain an upper bound on the number of edges in a bar k-visibility graph. As a consequence, we obtain an upper bound of 12 on the chromatic number of bar 1-visibility graphs, and a tight upper bound of 8 on the size of the largest complete bar 1-visibility graph. We conjecture ...
For each edge $uv\\\in E(G)$, the {\\\bf edge multiplicity} of $uv$ in $G$ is given by $m_G(uv)=|N_{G}(u)\\\cap N_{G}(v)|.$ For an integer $k$ with $k\\\ge 2$, a {\\\bf $k$-dense community} of a graph $G$, denoted by $DC_k(G)$, is a maximal...
Proof For Minimal Number of Edges Added to Make a Directed Graph Strongly Connected Link Can someone prove the correctness of the approach described in the first answer on the thread? I understand why the first step is crucial as a starting point. Thanks in advance!