Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where α is a real number (α 6= 0), and d(u) denotes the degree of the vertex u. In this paper, we present some new bounds for the connectivity index of a graph G in terms of the eigenvalues of the Laplacian matrix or adjacency matrix of the graph G, ...

Lengthy uninterrupted series of sections of the neural plexus in the compound eye of the horseshoe crab, Limulus polyphemus, have been used to reconstruct all the arborizations and their synaptic interconnections in a neuropil knot. This one microglomerulus contains the axons of 19 retinular cells, which pass by without contacts; 13 efferent fibres with 44 synapses to and from eccentric cell co...

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of ...

The Wiener index, denoted byW (G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, W (G) = 1 2 ∑ u,v∈V (G) d(u, v). In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

BACKGROUND The relevance of the remodeling pattern in the model of rats exposed to cigarette smoke is not known. OBJECTIVE Analyzing the presence of different remodeling patterns in this model and its relation with the ventricular function. METHODS Smoking rats (n=47) have been divided according to the geometry pattern, analyzed by echocardiogram: normal (normal mass index and normal relati...

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as ( ) ( ) ∑ u v u d v E G d x + ∈ and ( ) ( ) ∑ e u G v uv E d d = ∈ + respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Z...