منابع مشابه
On Spanning 2-trees in a Graph
A k-tree is either a complete graph on k vertices or a graph T that contains a vertex whose neighbourhood in T induces a complete graph on k vertices and whose removal results in a k-tree. A subgraph of a graph is a spanning k-tree if it is a k-tree and contains every vertex of the graph. This paper is concerned with spanning 2-trees in a graph. It is shown that spanning 2-trees have close conn...
متن کاملOn Central Spanning Trees of a Graph
We consider the collection of all spanning trees of a graph with distance between them based on the size of the symmetric difference of their edge sets. A central spanning tree of a graph is one for which the maximal distance to all other spanning trees is minimal. We prove that the problem of constructing a central spanning tree is algorithmically difficult and leads to an NP-complete problem.
متن کاملA Note on Leaf-constrained Spanning Trees in a Graph
An independent set S of a connected graph G is called a frame if G − S is connected. If |S| = k, then S is called a k-frame. We prove the following theorem. Let k ≥ 2 be an integer, G be a connected graph with V (G) = {v1, v2, . . . , vn}, and degG(u) denote the degree of a vertex u. Suppose that for every 3-frame S = {va, vb, vc} such that 1 ≤ a < b < c ≤ n, degG(va) ≤ a, degG(vb) ≤ b − 1 and ...
متن کاملSpanning Trees in 2-trees
A spanning tree of a graph G is a connected acyclic spanning subgraph of G. We consider enumeration of spanning trees when G is a 2-tree, meaning that G is obtained from one edge by iteratively adding a vertex whose neighborhood consists of two adjacent vertices. We use this construction order both to inductively list the spanning trees without repetition and to give bounds on the number of the...
متن کاملOn relation between the Kirchhoff index and number of spanning trees of graph
Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(96)00045-5