Antimagic labeling of the union of subdivided stars

Enomoto et al. (1998) defined the concept of a super (a, 0)-edge-antimagic total labeling and proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total labeling. In support of this conjecture, the present paper deals with different results on antimagicness of subdivided stars and their unions.Publisher's Versio

The Edge Version of Degree Based Topological Indices of HAC5C6C7[p, q] Nanotube

Let G be a simple molecular graph with vertex set V (G) and edge set E(G) respectively. The degree deg(v) of the vertex v 2 V (G) is the number of vertices adjacent with vertex v. A graph can be recognized by a numeric number, a polynomial, a sequence of numbers or a matrix. A topological index is a numeric quantity associated with a graph which characterize the topology of graph and is invariant under graph automorphism. Topological indices play important role in mathematical chemistry especially in the quantitative structurepropertyrelationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this paper we compute the edge version of some important degree based topological indices like Augmented Zagreb Index, Hyper-Zagreb Index, Harmonic Index and Sum-Connectivity Index of HAC5C6C7[p, q] Nanotube

M-Polynomials and degree-based Topological Indices of Some Families of Convex Polytopes

In this article, we compute closed forms of M-polynomial for three general classes of convex polytopes. From the M-polynomial, we derive degree-based topological indices such as first and second Zagreb indices, modified second Zagreb index, Symmetric division index, etc

Study of biological networks using graph theory

As an effective modeling, analysis and computational tool, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graph can express the molecular structure, where cell, gene or protein can be denoted as a vertex, and the connect element can be regarded as an edge. In this way, the biological activity characteristic can be measured via topological index computing in the corresponding graphs. In our article, we mainly study the biology features of biological networks in terms of eccentric topological indices computation. By means of graph structure analysis and distance calculating, the exact expression of several important eccentric related indices of hypertree network and X-tree are determined. The conclusions we get in this paper illustrate that the bioengineering has the promising application prospects. Keywords: Biological mathematics, DNA sequence, Biological networks, Topological inde

Computing Eccentricity Based Topological Indices of Octagonal Grid O n m

Graph theory is successfully applied in developing a relationship between chemical structure and biological activity. The relationship of two graph invariants, the eccentric connectivity index and the eccentric Zagreb index are investigated with regard to anti-inflammatory activity, for a dataset consisting of 76 pyrazole carboxylic acid hydrazide analogs. The eccentricity ε v of vertex v in a graph G is the distance between v and the vertex furthermost from v in a graph G. The distance between two vertices is the length of a shortest path between those vertices in a graph G. In this paper, we consider the Octagonal Grid O n m . We compute Connective Eccentric index C ξ ( G ) = ∑ v ∈ V ( G ) d v / ε v , Eccentric Connective Index ξ ( G ) = ∑ v ∈ V ( G ) d v ε v and eccentric Zagreb index of Octagonal Grid O n m , where d v represents the degree of the vertex v in G

Eccentricity-Based Topological Indices of a Cyclic Octahedron Structure

In this article, we study the chemical graph of a cyclic octahedron structure of dimension n and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index, the second Zagreb index, the third Zagreb index, the atom bond connectivity index and the geometric arithmetic index of the cyclic octahedron structure. Furthermore, we give the analytically closed formulas of these indices which are helpful for studying the underlying topologies

Margin based ontology sparse vector learning algorithm and applied in biology science

In biology field, the ontology application relates to a large amount of genetic information and chemical information of molecular structure, which makes knowledge of ontology concepts convey much information. Therefore, in mathematical notation, the dimension of vector which corresponds to the ontology concept is often very large, and thus improves the higher requirements of ontology algorithm. Under this background, we consider the designing of ontology sparse vector algorithm and application in biology. In this paper, using knowledge of marginal likelihood and marginal distribution, the optimized strategy of marginal based ontology sparse vector learning algorithm is presented. Finally, the new algorithm is applied to gene ontology and plant ontology to verify its efficiency

Topological Characterization of the Symmetrical Structure of Bismuth Tri-Iodide

The bismuth tri-iodide ( B i I 3 ) is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of the molecular graph that portray its topology and are normally graph invariants. In 1975, Randic presented, in a bond-added substance, a topological index as a descriptor for portraying subatomic branching. In this paper, we investigate the precious stone structure of bismuth tri-iodide chain and sheet. Moreover, exact formulas of degree-based added-substance topological indices principally the first, second, and hyper Zagreb indices, the general Randic index, the geometric-arithmetic index, the fourth atom-bond connectivity index, and the fifth geometric arithmetic index of the subatomic graph of bismuth tri-iodide for both chain and sheet structures are determined