Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

We investigate the following modification of the well known irregularity strength of graphs. Given a total weighting w of a graph G = (V,E) with elements of a set {1, 2, . . . , s}, denote wtG(v) = ∑ e3v w(e)+w(v) for each v ∈ V . The smallest s for which exists such a weighting with wtG(u) 6= wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of...

An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determined the exact values of the total e...

in this research, the effect of temperature on the physical and chemical behavior of nylon 66 tire cords in the range of 50-200°c and 16 h testing was studied. the results showed that heat treatment considerably reduced the breaking strength of cords. the intensity of reduction of breaking strength below 100°c and above 120°c was more pronounced than intermediate temperatures. the changes in pr...

A vertex (edge) irregular total k-labeling ? of a graph G is labeling the vertices and edges with labels from set {1,2,...,k} in such way that any two different (edges) have distinct weights. Here, weight x sum label all incident x, whereas an edge to edge. The minimum k for which has called irregularity strength G. In this paper, we are dealing infinite classes convex polytopes generated by pr...