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On minimal forbidden subgraphs for the class of EDM-graphsGašper Jaklič,
Jolanda Modic, 2015, original scientific article
Abstract: 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 ▫$n \le 8$▫ 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.
Keywords: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Published in RUP: 31.12.2021; Views: 938; Downloads: 20
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