[PDF] Top 20 Upper bounds for the number of spanning trees of graphs

... some upper bounds for the number of spanning trees of graphs in terms of the number of vertices, the number of edges and the vertex degrees of ...these upper ... See full document

... of graphs, where one can generate many new graphs from a given set of ...complexity, number of spanning trees, of some new join graphs, using linear algebra, Chebyshev ... See full document

... all graphs are ...A spanning tree in a graph G is a tree that has the same vertex set as ...the number of spanning trees τ(G) in a graph has an old history and has been very active ... See full document

... We consider simple finite non-empty graphs. For a graph G, its vertex and edge sets are denoted, respectively, by V (G) and E (G). We also use the following standard notation: d(v) for the degree of a vertex v in ... See full document

... the upper bounds of Theorems 4, 6, 8 and ...the upper bound of Theorem ...the upper bound for the double domination ...domination number, an interesting approximation algorithm was ... See full document

... polynomial bounds for the length of the shortest paths connection of two given markings for three classes of net systems: safe conflict- free systems, safe marked graphs, and live and safe extended ... See full document

... lower bounds for the number of vertices of graphs 2-cell embeddable on topological surfaces of a given ...stronger upper bounds for graphs with no triangles and graphs ... See full document

... smallest number of balls of resistance diameter ρ it takes to cover the nodes of ...line graphs) by building a binary tree on ...the number of nodes ...corresponding number of mistakes is the ... See full document

... the number of walks and closed walks in a ...several upper bounds for the number of closed walks in a graph in terms of the number of vertices, number of edges, maximum degree, ... See full document

... new upper bounds for the global domination and Roman domi- nation numbers and also prove that these results are asymptotically best ...give upper bounds for the restrained domination and total ... See full document

... i.e. upper and lower bounds and corresponding extremal ...and upper bounds for K f (G) of a connected (molecular) graph in terms of some structural graph parameters, such as the number ... See full document

... regular graphs of degree r. The first three bounds are sharp for complete graphs ...the number of spanning trees for regular ... See full document

... The upper bound 3 in Theorem ...2-connected graphs with proper connection number 3 ...connected graphs with proper connection number ...connection number of the graph G of Figure ... See full document

... real number and d(v) is the degree of vertex ...and upper bounds for the expected value and distribution function of this index in random increasing trees (recursive trees, ... See full document

... Abstract—We compare the lower bound of crossing number of bipartite and complete bipartite graph with Zarankiewicz conjecture and we illustrate the possible upper bound by a modified Zar[r] ... See full document

... the upper bounds for the Zagreb indices of n-vertex trees with given distance k-domination number and characterize the extremal trees, which generalize the results of Borovi´canin and ... See full document

... zero-forcing number, Z(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the ...for graphs with girth of at least 5; this can be further ... See full document

... weighted graphs, which are probed by means of discrete-time quantum ...complete graphs using discrete-time quantum walks is intractable due to the cost of simulating the quantum ...minimum spanning ... See full document

... Throughout this paper let us follow the terminology and notation of Harary [11]. Cockayne and Hedetniemi [7] introduce the concept dominating set. A subset S of vertices from V is called a dominating set for G if every ... See full document

... extremal graphs with respect to the Zagreb ...of graphs of chemical interest and emphasized that their "result leave open the question of the minimum values of Zagreb coindices over chemical ... See full document