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...

Consider a simple graph G with no isolated edges and at most one isolated vertex. A labeling w : E(G) → {1, 2, . . . ,m} is called product-irregular, if all product degrees pdG(v) = ∏ e3v w(e) are distinct. The goal is to obtain a product-irregular labeling that minimizes the maximum label. This minimum value is called the product irregularity strength. The analogous concept of irregularity str...

A total labeling of a graph G is a bijection from the vertex set and edge set of G onto the set {1, 2, . . . , |V (G)| + |E(G)|}. Such a labeling ξ is vertex-antimagic (edge-antimagic) if all vertex-weights wtξ(v) = ξ(v) + ∑ vu∈E(G) ξ(vu), v ∈ V (G), (all edge-weights wtξ(vu) = ξ(v) + ξ(vu) + ξ(u), vu ∈ E(G)) are pairwise distinct. If a labeling is simultaneously vertex-antimagic and edge-antim...

In this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. Let G = (V,E) be a graph with p vertices and q edges. G is said be skolem odd difference mean if there exists a function f : V (G) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : E(G) → {1, 3, 5, . . . , 2q−1} de...

Let be a graph with and are the set of its vertices edges, respectively. Total edge irregular -labeling on is map from to satisfies for any two distinct edges have weights. The minimum which labeling spoken as strength total labeling, represented by . In this paper, we discuss tes triangular grid graphs, spanning subgraphs, Sierpiński gasket graphs.

in this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. let g = (v,e) be a graph with p vertices and q edges. g is said be skolem odd difference mean if there exists a function f : v (g) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : e(g) → {1, 3, 5, . . . , 2q−1} d...

A function ϕ : V ( G )→{1, 2, …, k } of a simple graph is said to be non-inclusive distance vertex irregular -labeling if the sums labels vertices in open neighborhood every are distinct and an inclusive closed each different. The minimum for which has (resp. inclusive) called irregularity strength denoted by d i s ) ). In this paper, join product graphs investigated.