On the representation of abstract semigroups by transformation semigroups : Computer investigations.
È ben noto che fra le classi di sistemi ternari di Hall (HTS), gli HTS Abeliani ammettano una risoluzione siccome sono esattamente gli spazi affini finiti d'ordine 3; per questi sistemi una tal risoluzione è fornita dalla relazione di parallelismo. In questa nota viene dimostrato che certe classi di HTS non Abeliani costrutti dai gruppi di Burnside , anche ammettono una risoluzione. Allora, questi esempi di HTS si possono considerare anche come spazi finiti di Sperner e dunque la nota conclude...
The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.
Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. 56(131) (2006), 1207–1213) gave the definition of Laplacian energy of a graph and proved ; equality holds if and only if . In this paper we consider the relation between the Laplacian energy and the chromatic number of a graph and give an upper bound for the Laplacian energy on a connected graph.
Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ₂(G) and the second largest degree d₂(G), and present a sufficient condition for λ₂(G) ≥ d₂(G).
Let G be a graph. A function f : V (G) → {−1, 1} is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence function of G. In this paper, we present new bounds on these two parameters which improve some existing bounds....
A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply is ). Let denote the -shape tree obtained by identifying the end vertices of three paths , and . We prove that its all line graphs except () are , and determine the graphs which have the same signless Laplacian spectrum as . Let be the maximum signless Laplacian eigenvalue of the graph . We give the limit of , too.
A simplex of a graph G is a subgraph of G which is a complete graph. The simplex graph Simp(G) of G is the graph whose vertex set is the set of all simplices of G and in which two vertices are adjacent if and only if they have a non-empty intersection. The simplex graph operator is the operator which to every graph G assigns its simplex graph Simp(G). The paper studies graphs which are fixed in this operator and gives a partial answer to a problem suggested by E. Prisner.