Displaying similar documents to “On the minimum number of vertices and edges in a graph with a given number of spanning trees”

The Dynamics of the Forest Graph Operator

Suresh Dara, S.M. Hegde, Venkateshwarlu Deva, S.B. Rao, Thomas Zaslavsky (2016)

Discussiones Mathematicae Graph Theory

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In 1966, Cummins introduced the “tree graph”: the tree graph T(G) of a graph G (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge, i.e., two spanning trees T1 and T2 are adjacent if T2 = T1 − e + f for some edges e ∈ T1 and f ∉ T1. The tree graph of a connected graph need not be connected. To obviate this difficulty we define the “forest graph”: let G be a labeled graph of order α, finite...

L(2, 1)-Labelings of Some Families of Oriented Planar Graphs

Sagnik Sen (2014)

Discussiones Mathematicae Graph Theory

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In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.