2016/05/03 by Agnese Baldisserri, Baldisserri, Agnese, Elena Rubei +1
Computer Science · Engineering · Mathematics · #05C05 #05C12 #05C22 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1605.00946
openalex publication_date 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \cal G=(G,w) be a positive-weighted graph, that is a graph G endowed with a function w from the edge set of G to the set of positive real numbers; for any distinct vertices i,j , we define Di,j(\cal G) to be the weight of the path in G joining i and j with minimum weight. In this paper we fix a particular class of graphs and we give a criterion to establish whether, given a family of positive real numbers \DI\_I ∈ \1,...., n\ \choose 2, there exists a positive-weighted graph \cal G =(G,w) in the class we have fixed, with vertex set equal to \1,....,n\ and such that DI (\cal G) =DI for any I ∈ \1,...., n\ \choose 2. In particular, the classes of graphs we consider are the following: snakes, caterpillars, polygons, bipartite graphs, complete graphs, planar graphs.