OBJECTIVE To evaluate mandibular irregularity index stability following orthodontic treatment facilitated by alveolar corticotomy and augmentation bone grafting (Cort+). MATERIALS AND METHODS The irregularity index of 121 orthodontically treated and 15 untreated patient study casts was analyzed at 5 years and 10 years. RESULTS Cort+ resulted in significantly lower mandibular irregularity in...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

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 ...

A new formulation of Randić index is carried out as a minimization of a quadratic form which involves the Laplacian matrix of a graph. Using this formulation it is easy to realize that Randić index is useful in defining a new index of irregularity, which is then formulated here. A new context for the study of irregularity of graphs is advanced as a necessity for studying complex (biological) ne...

Despite abundant research on the distribution of glottal stops and glottalization in English and other languages, it is still unclear which factors matter most in predicting where glottal stops occur. In this study, logistic mixed-effects regression modeling is used to predict the occurrence of word-initial full glottal stops vs. no voicing irregularity. The results indicate that prominence and...

One of the important clinical features that differentiates benign melanocytic nevi from malignant melanomas is the irregularity of the lesion border. There are two types of border irregularities: texture irregularities, the small variations along the border, and structure irregularities, the global indentations and protrusions. Texture irregularities are subject to noise, whereas structure irre...

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...

The total irregularity of a simple undirected graphG is defined as irrt(G) = 1 2 ∑ u,v∈V (G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). Obviously, irrt(G) = 0 if and only if G is regular. Here, we characterize the non-regular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu, You and Yang [18] about the lower bound on the minimal ...