About Supergraphs. Part II

Pole DC	Wartość	Język
dc.contributor.author	Koch, Sebastian	-
dc.date.accessioned	2019-03-04T10:26:06Z	-
dc.date.available	2019-03-04T10:26:06Z	-
dc.date.issued	2018/07/01	-
dc.identifier.citation	Formalized Mathematics, Volume 26, Issue 2, Pages 125-140	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7622	-
dc.description.abstract	In the previous article [5] supergraphs and several specializations to formalize the process of drawing graphs were introduced. In this paper another such operation is formalized in Mizar [1], [2]: drawing a vertex and then immediately drawing edges connecting this vertex with a subset of the other vertices of the graph. In case the new vertex is joined with all vertices of a given graph G, this is known as the join of G and the trivial loopless graph K1. While the join of two graphs is known and found in standard literature (like [9], [4], [8] and [3]), the operation discribed in this article is not.Alongside the new operation a mode to reverse the directions of a subset of the edges of a graph is introduced. When all edge directions of a graph are reversed, this is commonly known as the converse of a (directed) graph.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	supergraph	-
dc.subject	graph operations	-
dc.title	About Supergraphs. Part II	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2018-0010	-
dc.description.Affiliation	Johannes Gutenberg University, Mainz, Germany	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	-
dc.description.references	Lowell W. Beineke and Robin J. Wilson, editors. Selected Topics in Graph Theory. Academic Press, London, 1978. ISBN 0-12-086250-6.	-
dc.description.references	John Adrian Bondy and U. S. R. Murty. Graph Theory. Graduate Texts in Mathematics, 244. Springer, New York, 2008. ISBN 978-1-84628-969-9.	-
dc.description.references	Sebastian Koch. About supergraphs. Part I. Formalized Mathematics, 26(2):101–124, 2018. doi:10.2478/forma-2018-0009.	-
dc.description.references	Gilbert Lee. Walks in graphs. Formalized Mathematics, 13(2):253–269, 2005.	-
dc.description.references	Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics,6(3):335–338, 1997.	-
dc.description.references	Klaus Wagner. Graphentheorie. B.I-Hochschultaschenbücher; 248. Bibliograph. Inst., Mannheim, 1970. ISBN 3-411-00248-4.	-
dc.description.references	Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd, Edinburgh, 1972. ISBN 0-05-002534-1.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	26	-
dc.description.issue	2	-
dc.description.firstpage	125	-
dc.description.lastpage	140	-
dc.identifier.citation2	Formalized Mathematics	-
dc.identifier.orcid	0000-0002-9628-177X	-
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