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Colin De Verdière Graph Invariant
Colin de Verdière's invariant is a graph parameter \mu(G) for any Graph (discrete mathematics), graph ''G,'' introduced by Yves Colin de Verdière in 1990. It was motivated by the study of the maximum multiplicity of the second eigenvalue of certain Schrödinger operators. Definition Let G=(V,E) be a simple graph with vertex set V=\. Then \mu(G) is the largest corank of any symmetric matrix M=(M_)\in\mathbb^ such that: * (M1) for all i,j with i\neq j: M_<0 if , and if ; * (M2) has exactly one negative eigenvalue, of multiplicity 1; * (M3) there is no nonzero matrix such that and such that if either or hold. Characterization of known graph families Several well-known families of graphs can be characterized in terms of their Colin de Verdièr ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Heawood Family
In graph theory the term Heawood family refers to either one of the following two related graph families generated via ΔY- and YΔ-transformations: * the family of 20 graphs generated from the complete graph K_7. * the family of 78 graphs generated from K_7 and K_. In either setting the members of the graph family are collectively known as Heawood graphs, as the Heawood graph is a member. This is in analogy to the Petersen family, which too is named after its member the Petersen graph. The Heawood families are significant in topological graph theory. They contain the smallest known examples of intrinsically knotted graphs, of graphs that are not 4-flat, and of graphs with Colin de Verdière graph invariant \mu=6. The K_7-family The K_7-family is generated from the complete graph K_7 through repeated application of ΔY- and YΔ-transformations. The family consists of 20 graphs, all of which have 21 edges. The unique smallest member, K_7, has seven vertices. The unique large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Combinatorica
''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, .... It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honorary editor-in-chief. The current editors-in-chief are Imre Bárány and József Solymosi. The advisory board consists of Ronald Graham, Gyula O. H. Katona, Miklós Simonovits, Vera Sós, and Endre Szemerédi. It is published by the János Bolyai Mathematical Society and Springer Verlag. The following members of the '' Hungarian School of Combinatorics'' have strongly contributed to the journal as authors, or have served as editors: Miklós Ajtai, László Babai, József Beck, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Proceedings Of The American Mathematical Society
''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. The journal is devoted to shorter research articles. As a requirement, all articles must be at most 15 printed pages. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 0.813. Scope ''Proceedings of the American Mathematical Society'' publishes articles from all areas of pure and applied mathematics, including topology, geometry, analysis, algebra, number theory, combinatorics, logic, probability and statistics. Abstracting and indexing This journal is indexed in the following databases: 2011. American Mathematical Society. * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Neil J
Neil is a masculine name of Irish origin. The name is an anglicisation of the Irish '' Niall'' which is of disputed derivation. The Irish name may be derived from words meaning "cloud", "passionate", "victory", "honour" or "champion".. As a surname, Neil is traced back to Niall of the Nine Hostages Niall Noígíallach (; Old Irish "having nine hostages"), or Niall of the Nine Hostages, was a legendary, semi-historical Irish king who was the ancestor of the Uí Néill dynasties that dominated Ireland from the 6th to the 10th centuries. ... who was an Irish king and eponymous ancestor of the Uí Néill and MacNeil kindred. Most authorities cite the meaning of Neil in the context of a surname as meaning "champion". Origins The Gaelic name was adopted by the Vikings and taken to Iceland as ''Njáll'' (see Nigel). From Iceland it went via Norway, Denmark, and Normandy to England. The name also entered Northern England and Yorkshire directly from Ireland, and from Norwegian sett ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
