A note on Nordhaus-Gaddum-type inequaliies for the automorphic H-chromatic index of graphs

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 which is preserved by a given automorphism H of G. We consider the sum and the product of the automorphic H-chromatic index of a graph and its complement. We prove upper and lower bounds in terms of the order of the graph when H is chosen to be either a cyclic group of prime order or a group of order four

Manifold Spines and Hyperbolicity Equations

We give a combinatorial representation of compact connected orientable 3-dimensional manifolds with boundary and their special spines by a class of graphs with extrastructure which are strictly related to o-graphs defined and studied in [3] and [4]. Then we describe a simple algorithm for constructing the boundary of these manifolds by using a list of 6-tuples of non-negative integers. Finally we discuss some combinatorial methods for determining the hyperbolicity equations. Examples of hyperbolic 3- manifolds of low complexity illustrate in particular cases the constructions and algorithms presented in the paper

Automorphic chromatic index of generalized Petersen graphs

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

Kite systems of order 8;Embedding of kite systems into bowtie systems

This article consist of two parts. In the first part, we enumerate the kite systems of order 8; in the second part, we consider embedding kite systems into bowtie systems

Balance, partial balance and balanced-type spectra in graph-designs

For a given graph G, the set of positive integers v for which a G-design exists is usually called the 'spectrum' for G and the determination of the spectrum is sometimes called the 'spectrum problem'. We consider the spectrum problem for G-designs satisfying additional conditions of 'balance', in the case where G is a member of one of the following infinite families of trees: caterpillars, stars, comets, lobsters and trees of diameter at most 5. We determine the existence spectrum for balanced G-designs, degree-balanced and partially degree-balanced G-designs, orbit-balanced G-designs. We also address the existence question for non-balanced G-designs, for G-designs which are either balanced or partially degree-balanced but not degree-balanced, for G-designs which are degree-balanced but not orbit-balanced

Some infinite classes of asymmetric nearly Hamiltonian snarks

We determine the full automorphism group of each member of three infinite families of connected cubic graphs which are snarks. A graph is said to be nearly hamiltonian if it has a cycle which contains all vertices but one. We prove, in particular, that for every possible order n ≥ 28 there exists a nearly hamiltonian snark of order n with trivial automorphism group

Basi di uno spazio vettoriale

Definizione di basi e dimensioni, Metodi per costruire basi e dimensioni, Teorema di Grassmann, Basi e matric

Balance in graph-designs

The notion of a balanced incomplete block design (BIBD) was generalized by Hell and Rosa to that of a balanced G-design on v vertices. For a given graph G, a G-design on v vertices is simply a G-decomposition of the complete graph K_v. A G-design is said to be balanced if there exists a constant r such that for each point x the number of blocks containing x is equal to r. Different conditions of ``balanced'' type can be defined by assuming that some other local parameter is a constant. In this vein one can define, for instance, orbit-balanced resp. degree-balanced G-designs. Some recent contributions on the following problems are considered: firstly, for each balanced-type condition determining the corresponding spectrum for a given graph G; secondly, in case some balanced-type spectra coincide for a given graph G, checking if the corresponding classes of balanced-type G-designs coincide as well

Misurazione e valutazione del processo educativo in un corso scientifico universitario

Si descrive come si pu\uf2 introdurre una misurazione e valutazione (alternativa) di un processo educativo in un corso scientifico universitario dell\u2019Universit\ue0 di Modena e Reggio Emilia che non stima solo ci\uf2 che lo studente ha acquisito dall\u2019insegnante ma valuta sia \u201ccome l\u2019allievo applica ci\uf2 che sa e crea\u201d sia \u201cil processo di apprendimento del discente\u201d. Si riporta un confronto tra due prove scritte, una strutturata e l\u2019altra semi- strutturata svolte in contemporanea sul medesimo argomento scientifico e dallo stesso studente. Bench\ue9 gli studenti sembrino acquisire risultati quantitativi apparentemente migliori con le prove strutturate, in termini di processo di apprendimento individuale le prove semi-strutturate risultano di maggiore e fondamentale importanza avendo una ricaduta profonda sia sull\u2019attivit\ue0 di apprendimento attivo svolto in aula, utilizzando come prima risorsa positiva gli errori degli studenti, sia sulla valutazione (alternativa)