R.P.Lewis, The number of spanning trees of a complete multipartite graph, Discrete Math. 197/198 (1999) 537-541R. P. Lewis, The number of spanning trees of a complete multipartite graph, Discrete Mathematics, 19
A spanning tree of a properly edge-colored complete graph, Kn, is rainbow provided that each of its edges receives a distinct color. In 1996, Brualdi and Hollingsworth conjectured that if K2m is properly (2m−1)-edge-colored, then the edges of K2m can be partitioned into m rainbow sp...
7. What is the minimum number of spanning tree(s) in a connected graph? 1 n nxn 0 Answer The correct answer is:A) 1 Explanation Every connected graph must have at least one spanning tree. Learn & Test Your Skills Python MCQsJava MCQsC++ MCQsC MCQsJavaScript MCQsCSS MCQsjQuery MCQsPHP...
[13] obtained upper bounds for the number of spanning trees of a connected graph. Using some ideas in [4], [5], and [13] and other established results, we obtain new upper bounds for the number of spanning trees of a connected graph. 关键词: Spanning Tree Laplacian Eigenvalue 年份:...
The Hamiltonian number of a connected graph is the length of a Hamiltonian walk . In other words, it is the minimum length of a closed spanning walk in the graph. For a Hamiltonian graph, , where is the vertex count. The Hamiltonian number therefore gives one measure of how far away a...
The optimal pebbling number of G, denoted by πopt(G), is the size of an optimal pebble distribution. In general, the decision problem for this graph parameter is NP-complete [5]. We denote with Pn and Cn the path and cycle on n vertices, respectively. The Cartesian productG◻H of...
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...
Graph Analysis of Functional Brain Topology Using Minimum Spanning Tree in Subjective Cognitive Decline Abstract:Background: Subjects with subjective cognitive decline (SCD) are proposed as a potential population to screen for Alzheimer’s disease (AD). Objective: Investigating brain topologies would help...
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Somatic copy number alterations (CNAs) are major mutations that contribute to the development and progression of various cancers. Despite a few computational methods proposed to detect CNAs from single-cell transcriptomic data, the technical sparsity of