All graphs in this paper are nontrivial and connected graph. Let 𝑓 ∶ 𝑉 (𝐺) → *1,2, … , 𝑘+ be a vertex coloring of a graph 𝐺where two adjacent vertices may be colored the same color. Consider the color classes Π = ...

Let G be a connected graph with E as edge set and V as vertex set . rm(v|W) = {d(v, s1), d(v, s2), . . . , d(v, sk)} is the multiset representation of a vertex v of G with respect to W where d(v, si) is a distance between ...

In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG(e, v) = min{d(x, v), d(y, v)} is the distance between the ...

Let G be a simple graph. A set of vertices, called V (G) and a set of edges, called E(G) are two sets which form graph G. W is a local adjacency resolving set of G if for every two distinct vertices x, y and x adjacent ...

An elegant labeling on graph G with vertices and edges is an injective (one-to-one) mapping from the set of vertices V (G) to the set of non-negative integers f0; 1; 2; 3; :::; g in such a way that the set of values ...

An elegant labeling on the graph G with n vertex and m edge is a one-to-one mapping (injection function) of the vertex set V (G) to the set of non negative integers {0, 1, 2, 3, . . . , m} such that each edge gets the ...

Let G = (V, E) be a graph with a vertex set V and an edge set E. The graph G is said to be with a local irregular vertex coloring if there is a function f called a local irregularity vertex coloring with the properties: ...

The meta-literacy ability is very important in today's life, especially living in the disruptive technology era. Meta-literacy is an ability that goes beyond metacognition and technological literacy. However, the students’ ...

Let a simple and connected graph G = (V, E) with the vertex set V (G) and the edge set E(G). If there is a mapping f: V (G) → 0, 2, . . . , 2kv and f: E(G) → 1, 2, . . . , ke as a function of vertex and edge irregularities ...