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Ljubljana Graph
In the mathematical field of graph theory, the Ljubljana graph is an undirected bipartite graph with 112 vertices and 168 edges. It is a cubic graph with diameter 8, radius 7, chromatic number 2 and chromatic index 3. Its girth is 10 and there are exactly 168 cycles of length 10 in it. There are also 168 cycles of length 12. Construction The Ljubljana graph is Hamiltonian and can be constructed from the LCF notation : [47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15, -49, 33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21, 31, -51, -25, 23, 9, -17, 51, 35, -29, 21, -51, -39, 33, -9, -51, 51, -47, -33, 19, 51, -21, 29, 21, -31, -39]2. The Ljubljana graph is the Levi graph of the Ljubljana configuration, a quadrangle-free configuration with 56 lines and 56 points. In this configuration, each line contains exactly 3 points, each point belongs to exactly 3 lines and any two lines intersect in at most one point. Algebraic properties The automorphism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covering Graph
In the mathematical discipline of graph theory, a graph is a covering graph of another graph if there is a covering map from the vertex set of to the vertex set of . A covering map is a surjection and a local isomorphism: the neighbourhood of a vertex in is mapped bijectively onto the neighbourhood of in . The term lift is often used as a synonym for a covering graph of a connected graph. Though it may be misleading, there is no (obvious) relationship between covering graph and vertex cover or edge cover. The combinatorial formulation of covering graphs is immediately generalized to the case of multigraphs. In the case of a multigraph with a 1-dimensional cell complex, a covering graph is nothing but a special example of covering spaces of topological spaces, so the terminology in the theory of covering spaces is available; say covering transformation group, universal covering, abelian covering, and maximal abelian covering. Definition Let ''G'' = (''V''1, ''E''1) and ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphism Group
In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is the group of invertible linear transformations from ''X'' to itself (the general linear group of ''X''). If instead ''X'' is a group, then its automorphism group \operatorname(X) is the group consisting of all group automorphisms of ''X''. Especially in geometric contexts, an automorphism group is also called a symmetry group. A subgroup of an automorphism group is sometimes called a transformation group. Automorphism groups are studied in a general way in the field of category theory. Examples If ''X'' is a set with no additional structure, then any bijection from ''X'' to itself is an automorphism, and hence the automorphism group of ''X'' in this case is precisely the symmetric group of ''X''. If the set ''X'' has additional struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slovenia
Slovenia ( ; sl, Slovenija ), officially the Republic of Slovenia (Slovene: , abbr.: ''RS''), is a country in Central Europe. It is bordered by Italy to the west, Austria to the north, Hungary to the northeast, Croatia to the southeast, and the Adriatic Sea to the southwest. Slovenia is mostly mountainous and forested, covers , and has a population of 2.1 million (2,108,708 people). Slovenes constitute over 80% of the country's population. Slovene, a South Slavic language, is the official language. Slovenia has a predominantly temperate continental climate, with the exception of the Slovene Littoral and the Julian Alps. A sub-mediterranean climate reaches to the northern extensions of the Dinaric Alps that traverse the country in a northwest–southeast direction. The Julian Alps in the northwest have an alpine climate. Toward the northeastern Pannonian Basin, a continental climate is more pronounced. Ljubljana, the capital and largest city of Slovenia, is geogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ljubljana
Ljubljana (also known by other historical names) is the capital and largest city of Slovenia. It is the country's cultural, educational, economic, political and administrative center. During antiquity, a Roman city called Emona stood in the area. Ljubljana itself was first mentioned in the first half of the 12th century. Situated at the middle of a trade route between the northern Adriatic Sea and the Danube region, it was the historical capital of Carniola, one of the Slovene-inhabited parts of the Habsburg monarchy. It was under Habsburg rule from the Middle Ages until the dissolution of the Austro-Hungarian Empire in 1918. After World War II, Ljubljana became the capital of the Socialist Republic of Slovenia, part of the Socialist Federal Republic of Yugoslavia. The city retained this status until Slovenia became independent in 1991 and Ljubljana became the capital of the newly formed state. Name The origin of the name ''Ljubljana'' is unclear. In the Middle Ages, both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tomaž Pisanski
Tomaž (Tomo) Pisanski (born 24 May 1949 in Ljubljana, Yugoslavia, which is now in Slovenia) is a Slovenian mathematician working mainly in discrete mathematics and graph theory. He is considered by many Slovenian mathematicians to be the "father of Slovenian discrete mathematics." Biography As a high school student, Pisanski competed in the 1966 and 1967 International Mathematical Olympiads as a member of the Yugoslav team, winning a bronze medal in 1967. He studied at the University of Ljubljana where he obtained a B.Sc, M.Sc and PhD in mathematics. His 1981 PhD thesis in topological graph theory was written under the guidance of Torrence Parsons. He also obtained an M.Sc. in computer science from Pennsylvania State University in 1979. Currently, Pisanski is a professor of discrete and computational mathematics and Head of the Department of Information Sciences and Technology at University of Primorska in Koper. In addition, he is a professor at the University of Ljubljana Fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dragan Marušič
Dragan Marušič (born 1953, Koper, Slovenia) is a Slovene mathematician. Marušič obtained his BSc in technical mathematics from the University of Ljubljana in 1976, and his PhD from the University of Reading in 1981 under the supervision of Crispin Nash-Williams. Marušič has published extensively, and has supervised seven PhD students (as of 2013). He served as the third rector of the University of Primorska from 2011-2019, a university he lobbied to have established in his home town of Koper. His research focuses on topics in algebraic graph theory, particularly the symmetry of graphs and the action of finite groups on combinatorial objects. He is regarded as the founder of the Slovenian school of research in algebraic graph theory and permutation groups. Education and career From 1968 to 1972 Marušič attended gymnasium in Koper. He studied undergraduate mathematics at the University of Ljubljana, graduating in 1976. He completed his PhD in 1981 in England, at the Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dejter Graph
In the mathematical field of graph theory, the Dejter graph is a 6-regular graph with 112 vertices and 336 edges.Borges J.; Dejter I. J. "On perfect dominating sets in hypercubes and their complements", J. Combin. Math. Combin. Comput. 20 (1996), 161-173Dejter I. J. "Symmetry of factors of the 7-cube Hamming shell", J. Combin. Des. 5 (1997), 301–309Dejter I. J.; Guan P. "Square-blocking edge subsets in hypercubes and vertex avoidance", Graph theory, combinatorics, algorithms, and applications (San Francisco, CA, 1989), 162–174, SIAM, Philadelphia, PA, 1991Dejter I. J.; Pujol J. "Perfect domination and symmetry in hypercubes", Proceedings of the Twenty-Sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, Florida, 1995). Congr. Numer. 111 (1995), 18–32Dejter I. J.; Weichsel P. M. "Twisted perfect dominating subgraphs of hypercubes", Proceedings of the Twenty-Fourth Southeastern International Conference on Combinatorics, Graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carsten Thomassen
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Carsten Thomassen may refer to: * Carsten Thomassen (mathematician) * Carsten Thomassen (journalist) Carsten Thomassen (15 May 1969 – 14 January 2008) was a Norway, Norwegian journalist, political commentator and war correspondent for the Norwegian daily newspaper ''Dagbladet''. He had earlier covered the 2004 Indian Ocean earthquake from Tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italo Jose Dejter
Italo Jose Dejter (December 17, 1939) is an Argentine-born American mathematician, a retired professor of mathematics and computer science from the University of Puerto Rico, (August 1984-February 2018) and a researcher in algebraic topology, differential topology, graph theory, coding theory and combinatorial designs. He obtained a Licentiate degree in mathematics from University of Buenos Aires in 1967, arrived at Rutgers University in 1970 by means of a Guggenheim Fellowship and obtained a Ph.D. degree in mathematics in 1975 under the supervision of Professor Ted Petrie, with support of the National Science Foundation. He was a professor at the Federal University of Santa Catarina, Brazil, from 1977 to 1984, with grants from the National Council for Scientific and Technological Development, (CNPq). Dejter has been a visiting scholar at a number of research institutions, including University of São Paulo, Instituto Nacional de Matemática Pura e Aplicada, Federal University of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andries Brouwer
Andries Evert Brouwer (born 1951) is a Dutch mathematician and computer programmer, Professor Emeritus at Eindhoven University of Technology (TU/e). He is known as the creator of the greatly expanded 1984 to 1985 versions of the roguelike computer game ''Hack'' that formed the basis for ''NetHack''. He is also a Linux kernel hacker. He is sometimes referred to by the handle ''aeb''. Biography Born in Amsterdam, Brouwer attended the gymnasium, and obtained his MSc in mathematics at the University of Amsterdam in 1971. In 1976 he received his Ph.D. in mathematics from Vrije Universiteit with a thesis entitled "Treelike Spaces and Related Topological Spaces", under the supervision of Maarten Maurice and Pieter Baayen, both of whom were in turn students of Johannes de Groot. In 2004 he received an honorary doctorate from Aalborg University. After graduation Brouwer started his academic career at the Mathematisch Centrum, later Centrum Wiskunde & Informatica. From 1986 to 2012 he w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marston Conder
Marston Donald Edward Conder (born 9 September 1955) is a New Zealand mathematician, a Distinguished Professor of Mathematics at Auckland University,Staff directory listing entry Auckland U. Mathematics, retrieved 22 January 2013. and the former co-director of the New Zealand Institute of Mathematics and its Applications. His main research interests are in , , and their connections with each other. Education and career Conder was born in |
110-vertex Iofinova-Ivanov Graph
Eleven or 11 may refer to: *11 (number), the natural number following 10 and preceding 12 * one of the years 11 BC, AD 11, 1911, 2011, or any year ending in 11 Literature * ''Eleven'' (novel), a 2006 novel by British author David Llewellyn *''Eleven'', a 1970 collection of short stories by Patricia Highsmith *''Eleven'', a 2004 children's novel in The Winnie Years by Lauren Myracle *''Eleven'', a 2008 children's novel by Patricia Reilly Giff *''Eleven'', a short story by Sandra Cisneros Music *Eleven (band), an American rock band * Eleven: A Music Company, an Australian record label *Up to eleven, an idiom from popular culture, coined in the movie ''This Is Spinal Tap'' Albums * ''11'' (The Smithereens album), 1989 * ''11'' (Ua album), 1996 * ''11'' (Bryan Adams album), 2008 * ''11'' (Sault album), 2022 * ''Eleven'' (Harry Connick, Jr. album), 1992 * ''Eleven'' (22-Pistepirkko album), 1998 * ''Eleven'' (Sugarcult album), 1999 * ''Eleven'' (B'z album), 2000 * ''Eleven'' (Reamonn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
