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Wiener–Araya Graph
The Wiener–Araya graph is, in graph theory, a graph on 42 vertices with 67 edges. It is hypohamiltonian, which means that it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian .... It is also Planar graph, planar. History Hypohamiltonian graphs were first studied by Sousselier in ''Problèmes plaisants et délectables'' (1963). In 1967, Lindgren built an infinite sequence of hypohamiltonian graphs. He first cited Gaudin, Herz and Rossi, then Busacker and Saaty as pioneers on this topic. From the start, the smallest hypohamiltonian graph is known: the Petersen graph. However, the hunt for the smallest Planar graph, planar hypohamiltonian graph continues. This question w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypohamiltonian Graph
In the mathematics, mathematical field of graph theory, a graph (discrete mathematics), graph ''G'' is said to be hypohamiltonian if ''G'' itself does not have a Hamiltonian cycle but every graph formed by removing a single vertex from ''G'' is Hamiltonian graph, Hamiltonian. History Hypohamiltonian graphs were first studied by . cites and as additional early papers on the subject; another early work is by . sums up much of the research in this area with the following sentence: “The articles dealing with those graphs ... usually exhibit new classes of hypohamiltonian or hypotraceable graphs showing that for certain orders ''n'' such graphs indeed exist or that they possess strange and unexpected properties.” Applications Hypohamiltonian graphs arise in integer programming solutions to the traveling salesman problem: certain kinds of hypohamiltonian graphs define Facet (mathematics), facets of the ''traveling salesman polytope'', a shape defined as the convex hull of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact facto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Adams
Douglas Noel Adams (11 March 1952 – 11 May 2001) was an English author, humorist, and screenwriter, best known as the creator of ''The Hitchhiker's Guide to the Galaxy''. Originally a 1978 BBC radio comedy, ''The Hitchhiker's Guide to the Galaxy'' evolved into a "trilogy" of six (or five, according to the author) books which sold more than 15 million copies in his life. It was made into a television series, several stage plays, comics, a video game, and a 2005 feature film. Adams's contribution to UK radio is commemorated in The Radio Academy's Hall of Fame. Adams wrote ''Dirk Gently's Holistic Detective Agency'' (1987) and '' The Long Dark Tea-Time of the Soul'' (1988), and co-wrote '' The Meaning of Liff'' (1983), '' The Deeper Meaning of Liff'' (1990) and '' Last Chance to See'' (1990). He wrote two stories for the television series ''Doctor Who'', including the unaired serial '' Shada'', co-wrote '' City of Death'' (1979), and served as script editor for its 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Hitchhiker's Guide To The Galaxy
''The Hitchhiker's Guide to the Galaxy'' is a Science fiction comedy, comedy science fiction franchise created by Douglas Adams. Originally a The Hitchhiker's Guide to the Galaxy (radio series), radio sitcom broadcast over two series on BBC Radio 4 between 1978 and 1980, it was soon adapted to other formats, including both novels and comic books; a The Hitchhiker's Guide to the Galaxy (TV series), 1981 BBC television series; a The Hitchhiker's Guide to the Galaxy (video game), 1984 text adventure game; stage shows; and a The Hitchhiker's Guide to the Galaxy (film), 2005 feature film. ''The Hitchhiker's Guide to the Galaxy'' is an international multimedia phenomenon; the novels are the most widely distributed, having been translated into more than 30 languages by 2005. The first novel, ''The Hitchhiker's Guide to the Galaxy (novel), The Hitchhiker's Guide to the Galaxy'' (1979), has been ranked fourth on the BBC's The Big Read poll. The sixth novel, ''And Another Thing... (no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phrases From The Hitchhiker's Guide To The Galaxy
''The Hitchhiker's Guide to the Galaxy'' is a comic science fiction series created by Douglas Adams that has become popular among fans of the genre and members of the scientific community. Phrases from it are widely recognised and often used in reference to, but outside the context of, the source material. Many writers on popular science, such as Fred Alan Wolf, Paul Davies, and Michio Kaku, have used quotations in their books to illustrate facts about cosmology or philosophy. The Answer to the Ultimate Question of Life, the Universe, and Everything is 42 In the radio series and the first novel, a group of hyper-intelligent pan-dimensional beings demand to learn the Answer to the Ultimate Question of Life, The Universe, and Everything from the supercomputer Deep Thought, specially built for this purpose. It takes Deep Thought million years to compute and check the answer, which turns out to be 42. Deep Thought points out that the answer seems meaningless because the being ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
42 (number)
42 (forty-two) is the natural number that follows 41 and precedes 43. Mathematics 42 is a pronic number, an abundant number as well as a highly abundant number, a practical number, an admirable number, and a Catalan number. The 42-sided ''tetracontadigon'' is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. 42 is the magic constant of the smallest non-trivial magic cube, a 3 \times 3 \times 3 cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two. 42 can be expressed as the sum of three cubes:80,435,758,145,817,515^3 + 12,602,123,297,335,631^3 + (-80,538,738,812,075,974)^3 = 42. Technology * Magic numbers used by programmers: ** In TIFF (Tag Image File Format), the second 16-bit word of every file is 42, "an arbitrary but carefully chosen number that further identifies the file as a TIFF file". ** In the reiser4 fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Graph Theory
The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. It is published by John Wiley & Sons. The journal was established in 1977 by Frank Harary.Frank Harary a biographical sketch at the ACM site The are [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, Nigel Hitchin, and Thomas Schick. Currently, the managing editor of Mathematische Annalen is Yoshikazu Giga (University of Tokyo). Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947, the journal briefly ceased publication. References External links''Mathematische Annalen''homepage a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
105-Thomassen Graph
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In mathematics The number 1 is the first natural number after 0. Each natural number, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with addit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
