the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the indu...

in this paper we initiate the study of real group algebras and investigate some of its aspects.let l1 (g) be a group algebra of a locally compact group g,τ :g →g be a group homeomorphismsuch that τ 2 =τοτ = 1, the identity map, and lp (g,τ ) = { f ∈ lp (g) : fοτ = f } ( p ≥ 1) . in thispaper, among other results, we clarify the structure of lp (g,τ ) and characterize amenability ofl1 (g,τ ) and...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

The paper investigates the value of using distinct vegetation indices to quantify and characterize agricultural crop characteristics at different growth stages. Research was conducted on four crops (corn, soybean, wheat, and canola) over eight years grown under different tillage practices and nitrogen management practices that varied rate and timing. Six different vegetation indices were found ...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...