No abstract

Let G=(V,E) be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from V∪E to {1,2,…,|V|+|E|} such that if for each uv∈E(G) then w(u)≠w(v), where w(u)=∑uv∈E(G)f(uv)+f(u). If the range set f satisfies f(V)={1,2,…,|V|}, then the labeling is said to be local super antimagic total labeling. This labeling generates a proper vertex coloring of the graph G with the color w(v) assigning the vertex v. The local super antimagic total chromatic number of graph G, χlsat(G) is defined as the least number of colors that are used for all colorings generated by the local super antimagic total labeling of G. In this paper we investigate the existence of the local super antimagic total chromatic number for some particular classes of graphs such as a tree, path, cycle, helm, wheel, gear, sun, and regular graphs as well as an amalgamation of stars and an amalgamation of wheels.

No abstract

Abstract. Let H be a simple and connected graph.

Abstract. We have developed a model for friction in a dry granular material, that allows multiple reversible transitions between stick and slip contacts. The ultimate purpose of the model is to simulate deposition processes. During these processes a pile structure is formed that is repeatedly destabilised by addition of new material. The present modeldoes not yet include rotation. The model is tested for a few simple systems. Finally we perform more extensive granular dynamics simulations using the model for 2D and 3D systems. In each system, a steady flow of material is dropped onto a rough surface.