let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

An edge-coloring of a graph G with natural numbers is called a sum edge-coloring if the colors of edges incident to any vertex of G are distinct and the sum of the colors of the edges of G is minimum. The edge-chromatic sum of a graph G is the sum of the colors of edges in a sum edge-coloring of G. It is known that the problem of finding the edge-chromatic sum of an r-regular (r ≥ 3) graph is N...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

Let G = (V,E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f : V → Z2 defined by f(v) ≡ ∑ uv∈E f(uv) (mod 2) for each v ∈ V , where Z2 = {0, 1} is the additive group of order 2. For i ∈ {0, 1}, let ef (i) = |f−1(i)| and vf (i) = |(f+)−1(i)|. A labeling f is called edge-friendly if |ef (1) − ef (0)| ≤ 1. If (G) = vf (1) − vf (0) is called the edge-friendly index o...

Graph labeling is considered as one of the most interesting areas in graph theory. A for a simple G (numbering or valuation), an association non -negative integers to vertices G  (vertex labeling) edges (edge both them. In this paper we study graceful k- uniform hypertree and define condition corresponding tree be graceful. if minimum difference vertices’ labels each edge dis...

Abstract : In this paper we introduced the concept of complementary super edge magic labeling and Complementary Super Edge Magic strength of a graph G.A graph G (V, E ) is said to be complementary super edge magic if there exist a bijection f:V U E → { 1, 2, ............p+q } such that p+q+1 f(x) is constant. Such a labeling is called complementary super edge magic labeling with complementary s...

This paper investigates optimal constellation labeling in the context of the edge profile. A constellation’s edge profile lists the minimum-distance edge for each binary symbol error. The paper introduces the symmetric-ultracomposite (SU) labeling structure and shows that this structure provides undominated edge profiles for 2 -PSK, 2 -PAM, and 2 -point square QAM. The SU structure is a general...

Suppose we label the vertices of a tree by positive integers. The weight of an edge is defined by a monotonically increasing function of the absolute value of the difference of the labels of its endpoints. We define the total cost of the labeling to be the sum of weights of all the edges. The problem we consider is that of determining for a given tree G and given a labeling of the leaves of G t...

For a simple graph G with vertex set V (G) and edge set E(G), a labeling φ : V (G) ∪ E(G) −→ {1, 2, . . . , k} is called a vertex irregular total klabeling of G if for any two different vertices x and y, their weights wt(x) ∗ The work was supported by the Higher Education Commission Pakistan. 148 A. AHMAD, K.M. AWAN, I. JAVAID AND SLAMIN and wt(y) are distinct. The weight wt(x) of a vertex x in...