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...

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...

We investigate several related measures of peripherality and centrality for vertices edges in networks, including the Mostar index which was recently introduced as a measure both networks. refute conjecture on maximum possible bipartite graphs. asymptotically answer another problem difference between irregularity trees. also prove number extremal bounds computational complexity results about in...

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.

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 ...