Showing papers on "Minimum degree spanning tree published in 1983"
Proceedings Article•
01 Jan 1983
TL;DR: Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph.
184 citations
129 citations
TL;DR: In this paper, the minimum number of edges a graph G on n vertices can have so that any tree on N vertices is isomorphic to some spanning tree of G, called such a graph universal for spanning trees.
Abstract: Introduction A number of papers [1,2,3,4,6] recently have been concerned with the following question. What is the minimum number s{n) of edges a graph G on n vertices can have so that any tree on n vertices is isomorphic to some spanning tree of G? We call such a graph universal for spanning trees. Since Kn, the complete graph on n vertices (see [5] for terminology), has the required property, it is immediate that
64 citations
TL;DR: A test of randomness based on the edge length distribution of the Minimal Spanning Tree is presented and it is shown that randomness is higher on the right side of the distribution than the left.
64 citations
TL;DR: In this article, a new and simpler method is proposed for counting the spanning trees of a labelled molecular graph, which involves finding the characteristic polynomials of certain graphs (the inner duals) related to, but substantially smaller than, the one whose spanning trees are being enumerated.
Abstract: A new and simpler method is proposed for counting the spanning trees of a labelled molecular-graph. Its application involves finding the characteristic polynomials (or generalized characteristic polynomials) of certain graphs (the inner duals) related to, but substantially smaller than, the one whose spanning trees are being enumerated.
45 citations
TL;DR: In this article, an algorithmic approach for transforming any spanning tree of a 2-connected graph into any other spanning tree in the graph is presented. But the approach is restricted to the case where the diameter of the spanning tree differs from that of the previous tree by at most one.
Abstract: We give an algorithmic approach for transforming any spanning tree of a 2-connected graph into any other spanning tree of the graph. At each step of the transformation we obtain a spanning tree whose diameter differs from that of the previous tree by at most one. Thus if a 2-connected graph G has a as the minimum and b as the maximum diameter of a spanning tree, then for any integer c between a and b , graph G has a spanning tree of diameter c .
35 citations
TL;DR: The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end-vertices, then for every integer k, m < k < n, G contains a spanning tree having exactly k end- Vertices.
Abstract: The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end-vertices, with m < n, then for every integer k, m < k < n, G contains a spanning tree having exactly k end-vertices. This settles a problem posed by Chartrand at the Fourth International Conference on Graph Theory and Applications held in Kalamazoo, 1980.
15 citations
01 Jan 1983
3 citations
TL;DR: A network-theoretic approach for counting the number of spanning trees of a graph based on a theorem in the theory of determinants, which results in a recurrence relation for counting Γn, the numberof spanning trees in a multigraph ladder having (n+1) nodes, is established.
Abstract: A network-theoretic approach for counting the number of spanning trees of a graph is proposed. This approach is based on a theorem in the theory of determinants. Following this approach, a recurrence relation for counting Γn, the number of spanning trees in a multigraph ladder having (n+1) nodes, is established. A recurrence relation is obtained connecting the sequences {Wn} and {Γn} where Wn is the number of spanning trees in a multigraph wheel having (n+1) nodes. The significance of the approach is further illustrated by giving simple proofs of certain well-known results, in particular, the formula for counting the number of spanning trees in a cascade of 2-port networks.
2 citations