Domination number and Laplacian eigenvalue distribution

Domination and Signed Domination Number of Cayley Graphs

In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.

Edge 2-rainbow domination number and annihilation number in trees

A edge 2-rainbow dominating function (E2RDF) of a graph G is a ‎function f from the edge set E(G) to the set of all subsets‎ ‎of the set {1,2} such that for any edge.......................

Semi - Group Domination and Eigenvalue Estimatesg

Semi-group Domination and Eigenvalue Estimates

For a class of integral operators it is shown that if the integral kernel of one operator majorates the kernel of the other one then certain forms of eigenvalue estimates are inherited. The operators must be related to a positivity preserving semi-group and, respectively, a positively dominated semi-group. It follows, in particular, that any, suuciently regular, eigenvalue estimate for the Schr...

The ∞−Laplacian first eigenvalue problem

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...