On the weights of simple paths in weighted complete graphs

Elena Rubei ()
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Elena Rubei: Dipartimento di Matematica “U. Dini”

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 4, 511-525

Abstract: Abstract Consider a weighted simple graph G on the vertex set {1,..., n}. For any path p in G, we call ω G (p) the sum of the weights of the edges of the path, and, for any {i, j} ⊂ {1,..., n}, we define the multiset $$D_{\{ i,j\} } (G) = \left\{ {\left. {w_G \left( p \right)} \right|p a simple path between i and j} \right\}.$$ We establish a criterion for a multisubset of ℝ to be of the form $$\mathcal{D}_{\{ i,j\} } (G)$$ for some weighted complete graph G and for some i, j vertices of G. Besides we establish a criterion for a family of multi-subsets of ℝ to be of the form for some weighted complete graph G with vertex set {1,..., n}.

Keywords: Graphs; weights of graphs (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0027-6

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