Namely, since our graph has to be connected, an arbitrary point p has to share an edge with at least one other point of V . Thus we only need to consider n − 1 (pos- sibly non-distinct) directions obtained by connecting p to all other points in V . Now consider the problem ...
graph G/uv/xy obtained by contraction of edges uv and xy in G is a 3-connected graph of minimum degree at least 4; (3) G has a vertex x with N(x) = {x(1), x(2), x(3), x(4)} and x(1)x(2), x(3)x(4) E(G) such that the graph (G - x)/x(1)x(2)/x(3...
Clearly, the oriented diameter of any bridgeless graph is at least two. Chvátal and Thomassen [4] proved that deciding if a given graph has an orientation of diameter two, and thus determining the oriented diameter, is NP-complete. Sufficient conditions for a graph to have an orientation of ...
a tree has one more vertex than edges, V = E+1. This is not true for the null graph. It makes sense to consider the null graph a forest, but not a tree, by convention, so that
connected graph withn(≥3)nodes and(n-1)edges lies between the sparsity indices of a Hamiltonian path and a star network of the same number of nodes and edges. In the process, the progression of the graphs to attain the lowest to the highest values of this index has been brought out ...
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+2). Mader [1] posed the following question: What is the maximum possible number of edges in...
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A graph is a mathematical structure consisting of vertices, edges, and a set of non-empty sets called circuits. A graph is connected if at least one path exists between every pair of vertices. A nontrivial circuit is a subset of vertices with no edges in common....
pIf the connected planar graph G is a 3-regular graph, which has 5 faces, then G has ___ edges. A. 6 B. 9 如何将EXCEL生成题库手机刷题 如何制作自己的在线小题库 > 手机使用 分享 反馈 收藏 举报 参考答案: B 复制 纠错 举一反三 MD系列算法和SHA系列算法是类似的,都采用MD迭代结构...
Let G be a graph on n vertices and H be an induced subgraph of G. H is called o-heavy if there are two nonadjacent vertices in H with degree sum at least n, and is called f-heavy if for every two vertices u,v∈V(H), dH(u,v)=2 implies that max{d(u),d(v)}≥n/2. ...