The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

Various structural factors that contribute to damage during an earthquake are vertical irregularities, irregularities in strength and stiffness, mass torsional so on. Over the past decade, performance-based design (PBD) procedures have become one of most critical areas engineering. The pushover procedure is divided into two parts; first displacement target for erected building. estimated top bu...

We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge wei...

Let G be a finite simple graph with v vertices and e edges. A vertex-magic total labeling is a bijection λ from V (G)∪E(G) to the consecutive integers 1, 2, · · · , v+e with the property that for every x ∈ V (G), λ(x) + Σy∈N(x)λ(xy) = k for some constant k. Such a labeling is super if λ(V (G)) = {1, · · · , v}. We study some of the basic properties of such labelings, find some families of graph...

A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The...

The study of graph labeling has focussed on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graph which admits a vertex magic total labeling. The class we considered here is the class of complete graphs, Kn . A vertex magic labeling of a graph is a bijection which maps the vertices V and edges E to the integers from 1, 2, 3, ...

Background an objective: Several studies have indicated that vertex type androgenetic alopecia have a higher-than-normal risk for coronary heart disease but few studies focused on lipid profiles which are important in the pathogenesis of coronary heart disease. This study was designed to investigate the relation between vertex type androgenetic alopecia (Grade III and higher according to ...

In this paper we introduce a new type of graph labeling, the (a, d)vertex-antimagic total labeling, which is a generalization of several other types of labelings. A connected graph G(V, E) is said to be (a, d)-vertex-antimagic total if there exist positive integers a, d and a bijection λ : V ∪ E → {1, 2, . . . , |V | + |E|} such that the induced mapping gλ : V → W is also a bijection, where W =...