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- W2346098750 abstract "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 $D_{i,j}({cal G})$ 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 ${D_I}_{I in { {1,...., n} choose 2}}$, 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 $D_I ({cal G}) =D_I$ for any $I in { {1,...., n} choose 2}$. In particular, the classes of graphs we consider are the following: snakes, caterpillars, polygons, bipartite graphs, complete graphs, planar graphs." @default.
- W2346098750 created "2016-06-24" @default.
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- W2346098750 creator A5073748449 @default.
- W2346098750 date "2016-05-03" @default.
- W2346098750 modified "2023-09-27" @default.
- W2346098750 title "Families of $2$-weights of some particular graphs" @default.
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