In the bipartite case k = 2, Lorenzini [11] calculated that (2) K(Kn1,n2) ∼ = (Z/n1Z) n2−2...R. P. Lewis, The number of spanning trees of a complete multipartite graph, Discrete Mathematics, 197/198(1999),
Abipartite-cylindrical drawingof the complete bipartite graphKm,nis a drawing on the surface of a cylinder, where the vertices are placed on the boundaries of the cylinder, one vertex-partition per boundary, and the edges do not cross the boundaries. Thebipartite-cylindrical crossing numberofKm,...
It is shown that for n≥141, among all triangle-free graphs on n vertices, the balanced complete bipartite graph K⌈n/2⌉,⌊n/2⌋ is the unique triangle-free graph with the maximum number of cycles. Using modified Bessel functions, tight estimates are given for the number of cycles...
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 ...
1431-all-ancestors-of-a-node-in-a-directed-acyclic-graph 1437-minimum-insertion-steps-to-make-a-string-palindrome 1456-find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance 1457-minimum-difficulty-of-a-job-schedule 1458-sort-integers-by-the-number-of-1-bits 1459...
Prove that a graph is bipartite if and only if it has no odd-length cycles. What is called finding the minimum spanning tree by starting at a random node and adding the node with the lowest weight link? Prove or disprove. Let G be a connected plane graph...
Binary tree is a special kind of tree where each node has a maximum of two children. The topmost node in the tree is called 'root' node. The left reference of the root node is called the 'left child' while the right reference is called the 'right child' of the ro...
In this paper, the author shows expressions for the numberι(K{sub}(n{sub}1, n{sub}2,…,n{sub}k)) of spanning trees in a complete k-partite graph K{sub}(n{sub}1, n{sub}2,…,n{sub}k)for some limited combinations of n{sub}1, n{sub}2,…,n{sub}k. The results are as...
 A Sharp Upper Bound for the Number of Spanning Trees of a Graph[J]. Graphs and Combinatorics . 2007 (6)K. C. Das, A sharp upper bound for the number of spanning trees of a graph, Graphs Combin. 23 (2007) 625-632.K.C. Das, A sharp upper bound...
to L+未, such that T~* is one ofminimum spanning trees under the length vector L+未 and the number of perturbed edges is minimum.This paper establishes a mathematical model for this problem and transforms it into a minimumvertex covering problem in a bipartite graph G_0, a path-graph. ...