A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

In this work, TiN/TiCN & PN/TiCN multilayer films were deposited by plasma- assisted chemical vapour deposition (PACVD). Plasma nitriding (PN) and TiN intermediate layer prior to coating leads to appropriate hardness gradient and it can greatly improve the mechanical properties of the coating. The composition, crystalline structure and phase of the films were investigated by X-ray d...

The reactions pn → dω and pn → dφ are studied within a relativistic meson-exchange model of hadronic interactions. Predictions for the total cross sections and for the angular distributions of the vector mesons are presented. The resulting cross sections near threshold are around 10-30 µb for pn → dω and 200-250 nb for pn → dφ. A moderate deviation of the cross section ratio σ pn→dφ /σ pn→dω fr...

Let G1∨G2 denote the graph obtained from G1+G2 by adding new edges from each vertex of G1 to every vertex of G2. In this paper, the critical groups of the graphs Km ∨ Pn (n ≥ 4) and Pm ∨ Pn (m ≥ 4, n ≥ 5) are determined.

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...