50,335 research outputs found
Three IndicesCalculationof Certain Crown Molecular Graphs
As molecular graph invariant topological indices, harmonic index, zeroth-order general Randic index and Co-PI index have been studied in recent years for prediction of chemicalphenomena. In this paper, we determine the harmonic index, zeroth-order general Randic index andCo-PI indexof certain r-crown molecular graphs
Harmonic index and harmonic polynomial on graph operations
Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O(n 2 ).This work was supported in part by two grants from Ministerio de EconomÃa y Competititvidad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain
New results on the harmonic index and its generalizations
In this paper we obtain new inequalities involving the harmonic index and the(general) sum-connectivity index, and characterize graphs extremal with respect tothem. In particular, we improve and generalize some known inequalities and werelate this indices to other well-known topological indices.The authors are grateful to the referees for their valuable comments which have improved this paper. This work is supported in part by two grants from Ministerio de EconomÃa y Competititvidad (MTM2013-46374-P and MTM2015-69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México
New Bounds for the Harmonic Energy and Harmonic Estrada index of Graphs
Let be a finite simple undirected graph with vertices and edges. The Harmonic energy of a graph , denoted by , is defined as the sum of the absolute
values of all Harmonic eigenvalues of . The Harmonic Estrada index of a graph , denoted by , is defined as
where are the - of .
In this paper we present some new bounds for and in terms of number of vertices, number of edges and the sum-connectivity index
Stable gonality is computable
Stable gonality is a multigraph parameter that measures the complexity of a
graph. It is defined using maps to trees. Those maps, in some sense, divide the
edges equally over the edges of the tree; stable gonality asks for the map with
the minimum number of edges mapped to each edge of the tree. This parameter is
related to treewidth, but unlike treewidth, it distinguishes multigraphs from
their underlying simple graphs. Stable gonality is relevant for problems in
number theory. In this paper, we show that deciding whether the stable gonality
of a given graph is at most a given integer belongs to the class NP, and we
give an algorithm that computes the stable gonality of a graph in
time.Comment: 15 pages; v2 minor changes; v3 minor change
Constant mean curvature surfaces in 3-dimensional Thurston geometries
This is a survey on the global theory of constant mean curvature surfaces in
Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight
canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2
\times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie
group Sol3. We will focus on the problems of classifying compact CMC surfaces
and entire CMC graphs in these spaces. A collection of important open problems
of the theory is also presented
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