منابع مشابه
The Number of Independent Dominating Sets of Labeled Trees
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A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-reduction process whereby a special type of subtree, called an e-graph, is collapsed to an edge. We show that genus is invariant under e-reduction. Our main result is a classification of genus one labeled circle trees t...
متن کاملA Bijective Proof for the Number of Labeled q-Trees
We giv e a bijective proof that the number of vertex labeled q-trees on n vertices is given by n q [ q n − q + 1 ] n − q − 2 . The bijection transforms each pair ( S , f ) where S is a q-element subset of an n-set, and f is a function mapping an ( n − q − 2 )-set to a ( q n − q + 1 )-set into a labeled q-tree on n nodes by a cutand-paste process. As a special case, q = 1 yields a new bi...
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In this paper we deal with k-arch graphs, a superclass of trees and k-trees. We give a recursive function counting the number of labeled k-arch graphs. Our result relies on a generalization of the well-known Prüfer code for labeled trees. In order to guarantee the generalized code to be a bijection, we characterize the valid code strings. A previous attempt at counting the number of labeled k-a...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80119-5