In this paper, we use a conformable fractional derivative GTα, with kernel Tfalse(t,αfalse)=efalse(α−1false)t, in order to study the fractional differential equation associated to a logistic growth model. As a practical application, we estimate the order of the derivative of the fractional logistic models, by solving an inverse problem involving real data. In the same direction, we show the feasibility of our approach with respect to the Ordinary, Khalil et al and Caputo approaches.

In this paper, we study the hyperbolicity constant of GG. In particular, we obtain upper and lower bounds for the hyperbolicity constant, and we compute its precise value for many graphs. Moreover, we obtain bounds and closed formulas for the general topological indices A(GG) = ∑ uv∈E(GG) a(d u , d v ) and B(GG) = ∑ u∈V(GG) b(d u ) (where d u denotes the degree of the vertex u, a is a symmetric function with real values, and b is a function with real values), and the generalized Wiener index W 𝜆 (GG), of complementary prisms networks. Finally, we performed a numerical study of the generalized Wiener index on random graphs.

A graph operator is a mapping F : Γ → Γ ′ , where Γ and Γ ′ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, Λ ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as δ ( G ) ≤ δ ( R ( G ) ) ≤ δ ( G ) + 1 / 2 , δ ( Λ ( G ) ) ≤ δ ( Q ( G ) ) ≤ δ ( Λ ( G ) ) + 1 / 2 , δ ( S ( G ) ) ≤ 2 δ ( R ( G ) ) ≤ δ ( S ( G ) ) + 1 and δ ( R ( G ) ) − 1 / 2 ≤ δ ( Λ ( G ) ) ≤ 5 δ ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.

Gromov hyperbolicity is an interesting geometric property, and so it is natural to study it in the context of geometric graphs. It measures the tree-likeness of a graph from a metric viewpoint. In particular, we are interested in circular-arc graphs, which is an important class of geometric intersection graphs. In this paper we give sharp bounds for the hyperbolicity constant of (finite and infinite) circular-arc graphs. Moreover, we obtain bounds for the hyperbolicity constant of the complement and line of any circular-arc graph. In order to do that, we obtain new results about regular, chordal and line graphs which are interesting by themselves.

Abstract:Gromov hyperbolicity is an interesting geometric property, and so it is natural to study it in the context of geometric graphs. In particular, we are interested in interval and indifference graphs, which are important classes of intersection and Euclidean graphs, respectively. Interval graphs (with a very weak hypothesis) and indifference graphs are hyperbolic. In this paper, we give a sharp bound for their hyperbolicity constants. The main result in this paper is the study of the hyperbolicity constant of every interval graph with edges of length 1. Moreover, we obtain sharp estimates for the hyperbolicity constant of the complement of any interval graph with edges of length 1.