A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, . . . , k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G...

—The localization accuracy of the conventional threedimensional (3D) node localization algorithm based on received signal strength (RSS) is restricted by the random signal strength fluctuation caused by the irregular propagation environments. In this paper, we propose an improved localization algorithm based on a differential RSS distance estimation algorithm to minimize the influence of the p...

A face irregular entire k-labeling φ : V ∪E ∪F → {1,2, . . . ,k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wφ ( f ) and wφ (g) are distinct. The weight of a face f under a k-labeling φ is the sum of labels carried by that face and all the edges and vertices incident with the face....

The El Niño/Southern Oscillation (ENSO) phenomenon is the dominant climatic fluctuation on interannual time scales. It is an irregular oscillation with a distinctive broadband spectrum. In this article, we discuss recent theories that seek to explain this irregularity. Particular attention is paid to explanations that involve the stochastic forcing of the slow ocean modes by fast atmospheric tr...

Let G = ( V , E ) be a simple undirected graph. A labeling f : )→{1, …, k } is local inclusive d -distance vertex irregular of if every adjacent vertices x y ∈ have distinct weights, with the weight w ), sum labels whose distance from at most . The irregularity strength lidis least number for which there exists In this paper, we prove conjecture on 1 tree and generalize result block graph using...