On minimal forbidden subgraphs for the class of EDM-graphs

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Title:	On minimal forbidden subgraphs for the class of EDM-graphs
Authors:	ID Jaklič, Gašper (Author) ID Modic, Jolanda (Author)
Files:	RAZ_Jaklic_Gasper_i2015.pdf (711,65 KB) MD5: 05131AF49490D4043EAE907394031086
Language:	English
Work type:	Unknown
Typology:	1.01 - Original Scientific Article
Organization:	ZUP - University of Primorska Press
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
Year of publishing:	2015
Number of pages:	str. 151-163
Numbering:	Vol. 9, no. 2
PID:	20.500.12556/RUP-17615
UDC:	519.17
ISSN on article:	1855-3966
COBISS.SI-ID:	17219417
Publication date in RUP:	31.12.2021
Views:	1546
Downloads:	21
Metadata:
:	JAKLIČ, Gašper and MODIC, Jolanda, 2015, On minimal forbidden subgraphs for the class of EDM-graphs. Ars mathematica contemporanea [online]. 2015. Vol. 9, no. 2, p. 151–163. [Accessed 8 April 2025]. Retrieved from: https://repozitorij.upr.si/IzpisGradiva.php?lang=eng&id=17615 Copy citation

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Title:	Ars mathematica contemporanea
Publisher:	Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:	1855-3966
COBISS.SI-ID:	239049984

Language:	Slovenian
Title:	On minimalnih prepovedanih podgrafih razreda EDM-grafov
Abstract:	V članku je obravnavana povezava med grafovsko razdaljnimi in evklidsko razdaljnimi matrikami (EDM). Obravnavani so grafi, katerih grafovsko razdaljne matrike niso EDM (NEDM-grafi). Analizirani so vsi enostavni povezani neizomorfni grafi z največ 8 vozlišči, podana pa je tudi karakterizacija najmanjših NEDM-grafov. Pokazano je, da so dvodelni grafi in nekatere subdivizije najmanjših NEDM grafov prav tako NEDM-grafi.
Keywords:	teorija grafov, graf, evklidsko razdaljna matrika, razdalja, lastna vrednost

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