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 ...

To explore whether differences in vitamin K nutrition might, at least in part, underlie differences in fracture incidence between Asian and European populations, the vitamin K status of older individuals in Shenyang, China (eighty-six men, ninety-two women) and in Cambridge, UK (sixty-seven men, sixty-seven women) was compared. Dietary information was collected by food questionnaire in Shenyang...

Let R be a commutative ring with Z(R) , its set of zero-divisors and Reg(R) , its set of regular elements. Total graph of R , denoted by T (Γ(R)) , is the graph with all elements of R as vertices, and two distinct vertices x, y ∈ R , are adjacent in T (Γ(R)) if and only if x+ y ∈ Z(R) . In this paper, some properties of T (Γ(R)) have been investigated, where R is a finite commutative ring and a...

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, in such a way that no two adjacent or incident elements receive the same color. A graph G is s-degenerated for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerated graph G has a total coloring with ∆ + 1 colors if the...

nonexchangeable soil-k release rate can significantly affect k dynamics and it's bioavailability during plant growth. in this study, twelve soil samples taken from different wheat cropping regions of iran were incubated with nabph4 to (i) investigate the kinetics of nonexchangeable k release and (ii) to compare the ability of various kinetic equations (zero-, first- and second-order, parab...

The k-th semi total point graph of a graph G, , ‎is a graph‎ obtained from G by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎In this paper‎, a formula for Laplacian polynomial of in terms of‎ characteristic and Laplacian polynomials of G is computed‎, ‎where is a connected regular graph‎.The Kirchhoff index of is also computed‎.

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...