منابع مشابه
A Partition of Connected Graphs
We define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize the set of graphs G such that k(G) = R. Because this set has a simple structure (it is isomorphic to a product of non-empty power sets), it is easy to evaluate certain graph invariants in terms of increasing trees. I...
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For a vertex v of a connected graph G and a subset S of V (G), the distance between v and S is d(v, S) = min{d(v, x)|x ∈ S}. For an ordered k-partition Π = {S1, S2, · · · , Sk} of V (G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v, S1), d(v, S2), · · · , d(v, Sk)). The k-partition Π is a resolving partition if the k-vectors r(v|Π), v ∈ V (G), are distinct. The minimu...
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We show that two results on covering of edge colored graphs by monochromatic connected parts can be extended to partitioning. We prove that for any 2-edgecolored non-trivial r-uniform hypergraph H, the vertex set can be partitioned into at most α(H)− r+ 2 monochromatic connected parts, where α(H) is the maximum size of a set of vertices that does not contain any edge. In particular, any 2-edgec...
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let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...
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where [x] denotes, as usual, the greatest integer not exceeding x. D. H. Lehmer [3] has investigated these sums on the basis of a different expression for the roots of unity involved. In the first place he factored the Akin) according to the prime powers contained in k. Secondly, by reducing them to sums studied by H. D. Kloosterman [4] and H. Salie [5], he evaluated the Ak(n) explicitly in the...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1968