It is possible to determine the optimum time for permanence of vegetative propagules (mini-cuttings) inside a greenhouse rooting, and this value can be used optimize structure nursery. The aim study was dynamics adventitious rooting in mini-cuttings three clones Eucalyptus benthamii x dunnii. Sprouts H12, H19 H20 were collected from mini-stumps that planted gutters containing sand grown semi-hydroponic system. basal region immersed 2,000 mg L-1 indole-3-butyric acid (IBA) solution 10...

A rotulação de grafos é um dos tópicos pesquisa em Teoria Grafos que associa elemento do grafo, como vértices ou arestas, a números inteiros denominados rótulos. Existem muitos trabalhos na literatura investigam problemas relacionados esse tópico. Dado grafo conexo G = (V, E) com ao menos três vértices, uma antimágica local bijeção f: E -> {1, 2, ..., |E|} induz, naturalmente, G, modo adjacentes não admitem o mesmo rótulo. menor quantidade rótulos induzidos por todas as rotulações...

Let G be a connected graph of order n, A(G) is the adjacency matrix and D(G) diagonal row-sums A(G). In 2017, Nikiforov [Nikiforov, V., Merging A- Q-Spectral Theories, Applicable Analysis Discrete Mathematics 11 (2017), pp. 81–107.] defined convex linear combinations Aα(G) byAα(G)=αD(G)+(1−α)A(G),0≤α≤1. this paper, we obtain partial factorization Aα-characteristic polynomial firefly which explicitly gives some eigenvalues graph.

Let G be a graph on n vertices and G? its complement. In this paper, we prove Nordhaus-Gaddum type inequality to the second largest eigenvalue of G, ?2(G), ?2(G) + ?2(G?) ? -1 n2/2-n+1, when is with girth at least 5. Also, show that bound above tight. Besides, result holds for some classes connected graphs such as trees, k-cyclic, regular bipartite complete multipartite graphs. Based these facts, conjecture our any graph.

There exist pentadiagonal matrices which are diagonally similar to symmetric matrices. In this work we describe explicitly the diagonal matrix that gives transformation for certain We also consider particular classes of and obtain recursive formulas characteristic polynomial explicit their eigenvalues.

Let G be a graph of order n, A(G) its adjacency matrix and D(G) the diagonal degrees G. In 2017, for every α in [0, 1], Nikiforov defined Aα(G) = αD(G) + (1 − α)A(G). this paper, we investigate Aα-spectrum graphs obtained from duplicate corona operations. As an application our results, provide conditions construction some pairs non isomorphic Aα-cospectral graphs.

Let G be a graph with adjacency matrix A(G) and let D(G) the diagonal of degrees G.For every real α ∈ [0, 1], Nikiforov [Applicable Analysis Discrete Mathematics, 11(1): 81-107, 2017] defined A (G) by = αD(G)+ (1-α)A(G).In this paper, we obtain eigenvalues some families graphs which have vertex connectivity equals to 1.

The Matrix-Tree Theorem is one of the classical theorems Algebraic Graph Theory.This proves a method counting trees that generate connected graph in terms eigenvalues or determinants matrices associated with such graphs.Theorem was first proved 1847 by German philosopher Gustav Kirchhoff his study electrical networks, and demonstrates relationship between generating matrices.There are several different proofs, generalizations, also some applications known.For example, Artur Cayley -a British...

The idea of the zero-divisor graph R, where R is a commutative ring with nonzero identity, was introduced by Beck in 1988, he mainly interested colorings R. Our definition denoted Γ(R), and emphasis on interplay between graph-theoretic properties Γ(R) ring-theoretic are due to Anderson Livingston 1999.Let be let Z * (R) set zero-divisors vertices such that there an edge x y if only = xy 0.In this work we will show some structural spectral F p 1 × 2 3 4 , pi field order i .More specifically,...

The eigenvalues of a graph are those its adjacency matrix.Recently, Cioabȃ, Haemers and Vermette characterized all graphs with but two equal to -2 0. In this article, we extend their result by characterizing explicitly in the interval [-2, 0].Also, determine among them that determined spectrum.

Let G be a graph with adjacency matrix A(G) and let D(G) the diagonal of degrees G. For every real α ∈ [0, 1], Nikiforov [21] Wang et al. [26] defined matrices Aα(G) Lα(G), respectively, as = αD(G)+(1−α)A(G) Lα(G) αD(G)+(α − 1)A(G). In this paper, we obtain some relationships between eigenvalues these for families graphs, part Aα Lα-spectrum spider display Lα-characteristic polynomials when their set vertices can partitioned into subsets that induce regular subgraphs. Moreover, determine...