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.

For a simple graph G with no isolated edges and at most, one vertex, labeling ?:E(G)?{1,2,…,k} of positive integers to the is called irregular if weights vertices, defined as wt?(v)=?u?N(v)?(uv), are all different. The irregularity strength known maximal integer k, minimized over labelings, set ? such exists. In this paper, we determine exact value modular fan graphs.

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 ...

M elanoma is associated with DNA damage and genomic alterations caused by ultraviolet light. In 2012, as part of efforts to better understand the causes of melanoma, researchers at the Broad Institute, the Dana-Farber Cancer Institute and a number of other institutes reported the results of whole genome sequencing of 25 human metastatic melanomas (Berger et al., 2012). This analysis discovered ...

One of the important clinical features to differentiate benign melanocytic nevi from malignant melanomas is the irregularity of the lesion border. A careful examination of a lesion border reveals two types of irregularity: texture irregularity and structure irregularity. Texture irregularities are the small variations along the border, while structure irregularities are the global indentations ...

Radio irregularity is a non-negligible phenomenon that has an impact on protocol performances. For instance, irregularity in radio range leads to asymmetric links that cause the loss of packets in different directions. In order to investigate its effect, the Radio Irregularity Model (RIM) is proposed that takes into account the irregularity of a radio range and estimates path losses in an aniso...

We investigate two modifications of the well-known irregularity strength of graphs, namely, a total edge irregularity strength and a total vertex irregularity strength. Recently the bounds and precise values for some families of graphs concerning these parameters have been determined. In this paper, we determine the exact value of the total edge (vertex) irregularity strength for the disjoint u...