It is easily observed that the vertices of a simple graph cannot have pairwise distinct degrees. This means no order at least two is, in this way, irregular. However, multigraph can be Chartrand et al., 1988, posed following problem: loopless multigraph, how one determine fewest parallel edges required to ensure all degrees? problem known as labeling and, for its solution, al. introduced irregu...

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary non-stationary patterns produced by two interacting populations is abundant in literature. Fragmented habitats are widespread reality due to irregularity landscape. This work considers a prey-predator model capable producing time-varying comple...

This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dis...

Irregularities are inherent to virtually all fibers, including the conventional textile fibers, the high-performance brittle fibers and newly developed nano-fibers. These irregularities can fall into two main categories: dimensional or geometrical irregularity (external) and structural irregularity (internal). For natural fibers such as wool, diameter variation along fiber length is atypical ex...

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 ...