منابع مشابه
Absolute algebraic connectivity of double brooms
We use a geometric technique based on embeddings of graphs to provide an explicit formula for the absolute algebraic connectivity and its eigenvectors of double brooms.
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متن کاملDegree Conditions for Spanning Brooms
A broom is a tree obtained by subdividing one edge of the star an arbitrary number of times. In [E. Flandrin, T. Kaiser, R. Kužel, H. Li and Z. Ryjáček, Neighborhood Unions and Extremal Spanning Trees, Discrete Math. 308 (2008), 2343-2350] Flandrin et al. posed the problem of determining degree conditions that ensure a connected graph G contains a spanning tree that is a broom. In this paper, w...
متن کاملAll Ramsey Numbers for Brooms in Graphs
For k, ` > 1, a broom Bk,` is a tree on n = k + ` vertices obtained by connecting the central vertex of a star K1,k with an end-vertex of a path on `− 1 vertices. As Bn−2,2 is a star and B1,n−1 is a path, their Ramsey number have been determined among rarely known R(Tn) of trees Tn of order n. Erdős, Faudree, Rousseau and Schelp determined the value of R(Bk,`) for ` > 2k > 2. We shall determine...
متن کاملCleaning Random d-Regular Graphs with Brooms
A model for cleaning a graph with brushes was recently introduced. Let α = (v1, v2, . . . , vn) be a permutation of the vertices of G; for each vertex vi let N (vi) = {j : vjvi ∈ E and j > i} and N−(vi) = {j : vjvi ∈ E and j < i}; finally let bα(G) = ∑n i=1 max{|N+(vi)|−|N−(vi)|, 0}. The Broom number is given by B(G) = maxα bα(G). We consider the Broom number of d-regular graphs, focusing on th...
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ژورنال
عنوان ژورنال: Nature
سال: 1962
ISSN: 0028-0836,1476-4687
DOI: 10.1038/1951261a0