Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sun, 25 Aug 2019 09:44:34 GMT2019-08-25T09:44:34Z10441Computing the automorphic chromatic index of certain snarkshttp://hdl.handle.net/11380/645430Titolo: Computing the automorphic chromatic index of certain snarks
Abstract: The automorphic H-chromatic index of agraph G is the minimum integer m for which G has aproper edge-coloring with m colors which is preserved by the fullautomorphism group H of G. We determine the automorphic H-chromatic index of eachmember of four infinite classes of snarks: type I Blanu\v{s}asnarks, type II Blanu\v{s}a snarks, Flower snarks and Goldbergsnarks.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6454302010-01-01T00:00:00ZUpper bounds for the automorphic chromatic index of a graphhttp://hdl.handle.net/11380/1060574Titolo: Upper bounds for the automorphic chromatic index of a graph
Abstract: The automorphic H-chromatic index of a graph G is the
minimum integer m for which G has a proper edge-coloring
with m colors preserved by a given subgroup H of the full
automorphism group of G. We determine upper bounds for this index
in terms of the chromatic index of G for some abelian 2-groups H.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10605742014-01-01T00:00:00ZAutomorphic chromatic index of generalized Petersen graphshttp://hdl.handle.net/11380/625856Titolo: Automorphic chromatic index of generalized Petersen graphs
Abstract: The automorphic A-chromatic index of agraph G is the minimum integer m for which G has aproper edge-coloring with m colors which is preserved by a givensubgroup A of the full automorphism group of G. We computethe automorphic A-chromatic index of each generalized Petersengraph when A is the full automorphism group.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6258562009-01-01T00:00:00ZMatrici, Ranghi e Sistemi Linearihttp://hdl.handle.net/11380/1164136Titolo: Matrici, Ranghi e Sistemi Lineari
Abstract: Questo fascicolo fa parte di una serie di fascicoli (si veda bibliografia interna) di Matematica della Teoria di Algebra Lineare e tratta della Teoria delle Matrici, dei Ranghi e dei Sistemi Lineari. L’ultima parte trattata da codesto fascicolo presuppone l’acquisizione di alcune nozioni di Algebra Lineare, tutte già affrontate nei fascicoli precedentemente pubblicati. La novità di questo fascicolo rispetto agli altri risulta in una trattazione sistematica della Teoria delle Matrici, dei Ranghi e dei Sistemi Lineari il cui sviluppo nei Libri di Algebra Lineare si trova svolto in maniera frammentato in quanto presuppone lo svolgimento (tra un argomento e l’altro) di altri concetti: lineare indipendenza, dimensione di sottospazi vettoriali, determinanti etc.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11380/11641362018-01-01T00:00:00ZCyclic branched coverings of 2-bridge knotshttp://hdl.handle.net/11380/12838Titolo: Cyclic branched coverings of 2-bridge knots
Abstract: In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11380/128381999-01-01T00:00:00ZA survey on snarks and new results: Products, reducibility and a computer searchhttp://hdl.handle.net/11380/309541Titolo: A survey on snarks and new results: Products, reducibility and a computer search
Abstract: In this paper we survey recent results and problems of both theoretical and algorithmic character on the construction of snarks-non-trivial cubic graphs of class two, of cyclic edge-connectivity at least 4 and with girth greater than or equal to 5. We next study the process, also considered by Cameron, Chetwynd, Watkins, Isaacs, Nedela, and Skoviera, of splitting a snark into smaller snarks which compose it. This motivates an attempt to classify snarks by recognizing irreducible and prime snarks and proving that all snarks can be constructed from them. As a consequence of these splitting operations, it follows that any snark (other than the Petersen graph) of order less than or equal to 26 can be built as either a dot product or a square product of two smaller snarks. Using a new computer algorithm we have confirmed the computations of Brinkmann and Steffen on the classification of all snarks of order less than 30. Our results recover the well-known classification of snarks of order not exceeding 22. Finally, we prove that any snark G of order less than or equal to 26 is almost Hamiltonian, in the sense that G has at least one vertex v for which G\v is Hamiltonian.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/11380/3095411998-01-01T00:00:00ZDecomposing four-manifolds up to homotopy typehttp://hdl.handle.net/11380/309535Titolo: Decomposing four-manifolds up to homotopy type
Abstract: Let M be a closed connected oriented topological 4-manifold. Suppose that there is a degree one map f from M to another closed topological 4-manifold P, which induces an isomorphism between the fundamental groups. We give a homological condition on the integer intersection form of M and on the intersection form of M over the integral group ring of its fundamental group under which M is homotopy equivalent to a connected sum of P with a simply-connected closed topological 4-manifold M'. This gives a partial solution to a conjecture of Hillman stated in Bull. London Math. Soc. 27 (1995). Then some splitting results for closed 4-manifolds with special homotopy complete the paper.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/3095352003-01-01T00:00:00ZInfinite classes of dihedral snarkshttp://hdl.handle.net/11380/611850Titolo: Infinite classes of dihedral snarks
Abstract: Flower snarks and Goldberg snarks are two infinite families of cyclically 5-edge-connected cubic graphs with girth at least five and chromatic index four. For any odd integer k, k>3, there is a Flower snark, say J_k, of order 4k and a Goldberg snark, say B_k, of order 8k. We determine the automorphic groups of J_k and B_k for every k and prove that they are isomorphic to the dihedral group D_4k of order 4k.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/6118502008-01-01T00:00:00ZBalance, partial balance and balanced-type spectra in graph-designshttp://hdl.handle.net/11380/1124297Titolo: Balance, partial balance and balanced-type spectra in graph-designs
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/11242972015-01-01T00:00:00ZOn the automorphic chromatic index of a graphhttp://hdl.handle.net/11380/644808Titolo: On the automorphic chromatic index of a graph
Abstract: We define the automorphic H-chromatic index of a graph G as the minimum integer m for which G has a proper edge-coloring with m colors which is preserved by a given automorphism group H of G. After the description of some properties, we determine upper bounds for this index when H is a cyclic group of prime order. We also show that these upper bounds are best possible in a number of istances.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/6448082008-01-01T00:00:00Z