‎The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$‎ ‎such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial‎ ‎automorphism‎. ‎For any $n in mathbb{N}$‎, ‎the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...

a graph g = (v,e) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : v (g) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ v (g), xy ∈ e(g), and the total number of 0, 1 and 2 are balanced. that is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). in thi...

Let G be a graph with p vertices and q edges an injective function, where k is positive integer. If the induced edge labeling defined by for each bijection, then f called odd Fibonacci irregular of G. A which admits graph. The irregularity strength ofes(G) minimum labeling. In this paper, some subdivision graphs obtained from vertex identification determined.

Graphs that have the properties of odd harmonious labeling are graphs. The research objective this paper is to obtain on layered graph C(x,y) and D(x,y). used in a qualitative method. flow consists data collection, processing, analysis. collection stage constructing definition new class graph, processing vertex edge labeling, analysis theorem proving it. results show D(x,y) fulfill labeling. Su...