On centroid branches of trees from certain families
نویسندگان
چکیده
منابع مشابه
On the Wiener index of trees from certain families
The Wiener index W( G) of a connected graph G is the sum of the distances d( u, v) between all pairs of vertices u and v of G. This index seems to have been introduced in [22] where it was shown that certain physical properties of various paraffin species are correlated with the Wiener index of the tree determined by the carbon atoms of the corresponding molecules. Canfield, Robinson, and Rouvr...
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The Steiner distance dc(S) of a subset S of nodes of a connected graph G is the minimum number of edges in a connected subgraph of G that contains S. We consider the behaviour of the expected value ILk (n) of dT(S) and the probability Pk(n, m) that dT(S) rn lover all subsets S of k nodes of trees T of order n from certain families of trees.
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Sufficient conditions are given in terms of S(G) and A(T), for a graph G with n vertices to contain a tree T with n vertices. One of these sufficient conditions is used to calculate some of the Ramsey numbers for the pair tree-star. Also necessary conditions are given, in terms of d(G), for a graph G with n vertices to contain all trees with n vertices .
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It follows from our results that as n → ∞ the average distance between the root and the (nearer) centroid node of a recursive tree Tn tends to 1; and the average value of the label of the (nearer) centroid node tends to 5/2.
متن کاملPacking and covering constants for certain families of trees. I
In an earlier paper we considered the problem of determining the packing and covering constants for families of trees whose generating function^ satisfied a relation y = x(y) for some power series itiy. In the present paper we consider the problem for some families of trees whose generating functions satisfy a more complicated relation.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00280-1