Geodesic
On minimal forbidden subgraphs for the class of EDM-graphs
Ars Mathematica Contemporanea, Tome 9 (2015) no. 2, pp. 151-163.

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In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. Graphs, for which the distance matrix is not an EDM (NEDM-graphs), are studied. All simple connected non-isomorphic graphs on n = 8 nodes are analysed and a characterization of the smallest NEDM-graphs, i.e., the minimal forbidden subgraphs, is given. It is proven that bipartite graphs and some subdivisions of the smallest NEDM-graphs are NEDM-graphs, too.
DOI : 10.26493/1855-3974.467.98f
Keywords: Graph, Euclidean distance matrix, distance, eigenvalue. 
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Gašper Jaklič; Jolanda Modic. On minimal forbidden subgraphs for the class of EDM-graphs. Ars Mathematica Contemporanea, Tome 9 (2015) no. 2, pp. 151-163. doi : 10.26493/1855-3974.467.98f. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.467.98f/

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