DSpace collection:
http://ria.ua.pt:80/handle/10773/5868
Sun, 22 Apr 2018 07:00:01 GMT2018-04-22T07:00:01ZOn the higher differentiability of solutions to a class of variational problems of fast growth
http://ria.ua.pt:80/handle/10773/22744
title: On the higher differentiability of solutions to a class of variational problems of fast growth
authors: Cellina, Arrigo; Staicu, Vasile
abstract: We consider the higher differentiability of a solution $u$ to the problem of minimizing $$\int_{\om}[\Lambda(x ,|\nabla v(x)|) +f(x)v(x)]dx$$
where $\Lambda$ is of fast growth in the second variable, i.e., we assume that $\Lambda(x,t)$ grows in $t$ faster than $t^N$, where $N$ is the dimension of the space. We do not assume conditions limiting above the size of the second derivative of $\Lambda$ with respect to $t$.Thu, 15 Mar 2018 00:00:00 GMThttp://ria.ua.pt:80/handle/10773/227442018-03-15T00:00:00ZA sharp lower bound on the signless Laplacian index of graphs with (k,t)-regular sets
http://ria.ua.pt:80/handle/10773/22568
title: A sharp lower bound on the signless Laplacian index of graphs with (k,t)-regular sets
authors: Andelic, Milica; Cardoso, Domingos M.; Pereira, António
abstract: A new lower bound on the largest eigenvalue of the signless
Laplacian spectra for graphs with at least one
$(\kappa,\tau)$-regular set is introduced and applied to the
recognition of non-Hamiltonian graphs or graphs without a perfect
matching. Furthermore, computational experiments revealed that the
introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).Sat, 03 Mar 2018 00:00:00 GMThttp://ria.ua.pt:80/handle/10773/225682018-03-03T00:00:00ZOn the dominating induced matching problem: Spectral results and sharp bounds
http://ria.ua.pt:80/handle/10773/22566
title: On the dominating induced matching problem: Spectral results and sharp bounds
authors: Andrade, Enide; Cardoso, Domingos M.; Medina, Luis; Rojo, Oscar
abstract: A matching M is a dominating induced matching of a graph if every edge is either in M or has a common end-vertex with exactly one edge in M. The extremal graphs on the number of edges with dominating induced matchings are characterized by its Laplacian spectrum and its principal Laplacian eigenvector. Adjacency, Laplacian and signless Laplacian spectral bounds on the cardinality of dominating induced matchings are obtained for arbitrary graphs. Moreover, it is shown that some of these bounds are sharp and examples of graphs attaining the corresponding bounds are given.Mon, 01 Jan 2018 00:00:00 GMThttp://ria.ua.pt:80/handle/10773/225662018-01-01T00:00:00ZSpectra, signless Laplacian and Laplacian spectra of complementary prisms of graphs
http://ria.ua.pt:80/handle/10773/22565
title: Spectra, signless Laplacian and Laplacian spectra of complementary prisms of graphs
authors: Cardoso, Domingos M.; Carvalho, Paula; Freitas, Maria Aguieiras A. de; Vinagre, Cybele T.M.
abstract: The complementary prism GG‾ of a graph G is obtained from the disjoint union of G and its complement G‾ by adding an edge for each pair of vertices (v,v′), where v is in G and its copy v′ is in G‾. The Petersen graph C5C5‾ and, for n≥2, the corona product of Kn and K1 which is KnKn‾ are examples of complementary prisms. This paper is devoted to the computation of eigenpairs of the adjacency, signless Laplacian and Laplacian matrices of a complementary prism GG‾ in terms of the eigenpairs of the corresponding matrices of G. Particular attention is given to the complementary prisms of regular graphs. Furthermore, Petersen graph is shown to be the unique complementary prism which is a strongly regular graph.Wed, 07 Mar 2018 00:00:00 GMThttp://ria.ua.pt:80/handle/10773/225652018-03-07T00:00:00Z