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.

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.

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

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...

This study investigated the change in interproximal force (IPF) in mandibular anterior teeth during retention and the relationship between the irregularity index before orthodontic treatment and the IPF. The effect that an erupting third molar had on IPF was also examined. Forty treated patients (40 with extraction of four bicuspids) were followed for 18 months during the retention phase. The i...

In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

BACKGROUND/PURPOSE The Irregularity Index is a measure of border irregularity from pigmented skin lesion images. The measure attempts to quantify the degree of irregularity of the structural indentations and protrusions along a lesion border. A carefully designed study has shown that the parameters derived from the Irregularity Index were highly correlated with expert dermatologists' notion of ...

Cutaneous melanocytic lesions, commonly known as moles, are mostly benign; however, some of them are malignant melanomas, the most fatal form of skin cancer. Because the survival rate of melanoma is inversely proportional to the thickness of the tumor, early detection is vital to the treatment process. Many dermatologists have advocated the development of computer-aided diagnosis systems for ea...