Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties, such as melting and boiling points, toxicity and resistance. Here we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees and the Collat...

The irregularity of a graph G is defined as the sum of weights |d(u) − d(v)| of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, some structural properties on trees with maximum (or minimum) irregularity among trees with given degree sequence and trees with given branching number are explored, respectively. Moreover, the correspon...

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...

[1] Based on the analysis of a low-order tropical atmosphere-ocean model we propose a nonlinear mechanism explaining several features of the observed El Niño-Southern Oscillation (ENSO) phenomenon: ENSO irregularity, ENSO Amplitude Modulations and decadal tropical climate variability. The mechanism suggested here is based on the idea of homoclinic/heteroclinic orbits, an inherently nonlinear co...

The small GTPase Rho and one of its targets, Rho-associated kinase (ROCK), participate in a variety of actin-based cellular processes including smooth muscle contraction, cell migration, and stress fiber formation. The ROCK protein consists of an N-terminal kinase domain, a central coiled-coil domain containing a Rho binding site, and a C-terminal pleckstrin homology domain. Here we present the...

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.