the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.

The local antimagic total vertex labeling of graph G is a that every vertices and edges label by natural number from 1 to such two adjacent has different weights, where sum the labels all incident vertex. If start smallest then edge so kind coloring called super labeling. That induces for v, weight w(v) color v. minimum colors obtained chromatic G, denoted χlsat(G). In this paper, we consider G...

solution potassium (so-k) and exchangeable k (ex-k) extracted by nh4oac are the major sources of potassium used by plants, but initially non-exchangeable k (nex-k) can also contribute significantly to plant uptake. perennial ryegrass (lolium perenne, cv. roper) was successively planted in ten surface soil samples with different clay mineralogical composition belonging to five soil types to dete...

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-d...

Let G be a graph with vertex set V (G), and let f : V (G) −→ {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑ x∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that ∑d i=1 fi(x) ≤ k for each x ∈ V (G), is call...

We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each k ∈ Z+ we introduce a payoff function, called the k-total reward. For k = 0 and 1 these payoffs are known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case, the so called cyclic games. For all k, we prove the existence of a saddle point which can be rea...