2012/10/02 by Elena Rubei, Rubei, Elena
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1210.0845
openalex publication_date 2012/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a weighted graph G with n vertices, numbered by the set 1,...,n. For any path p in G, we call wG(p) the sum of the weights of the edges of the path and we define the multiset \cal Di,j (G) = wG(p) | p simple path between i and j We establish a criterion to say when, given a multisubset of the set of the real numbers there exists a weighted complete graph G such that the multisubset is equal to \cal Di,j (G) for some i,j vertices of G. Besides we establish a criterion to say when, given for any i, j in 1,...,n a multisubset of the set of the real numbers,\cal Di,j, there exists a weighted complete graph G with vertices 1,...,n such that \cal Di,j (G)= \cal Di,j for any i,j.