All graphs in this paper is connected and simple. Let ( ) be a connected and simple graph with vertices set and edge set . A bijection function * | ( )|+ is called an edge antimagic vertex ...

All graph in this paper is connected and simple graph. Let du,v be a distance between any vertex u and v in graph G  V,E . A function c :VG1, 2,, k is called a packing k-coloring if every two vertices ...

A function f is called a local irregularity vertex coloring if (i) l : V (G) ! f1; 2; ; kg as vertex irregular k-labeling and w : V (G) ! N, for every uv 2 E(G); w(u) 6= w(v) where w(u) = v2N(u)l(v) and (ii) ...

For a set W = { s1,s2,...,sk of vertices of a graph G, the representation multiset of a vertexv of G with respect to W is r(v | W ) = { d(v, s1),d(v, s2),...,d(v, sk) } , where d(v, si) is a distance between of ...

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 = ...

In this paper we will study the r-dynamic chromatic number of the coronation by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v receive at least minfr; d(v)g di®erent colors. The ...

e a simple, connected undirected graph with m vertices and n edges. Let ver tex coloring c of a graph G be a mapping c : V (G) → S, where |S| = k and it is k-colorable. Vertex coloring is proper if none of the any two ...

Let G = (V,E) be a simple, finite, undirected, and connected graph with vertex set V (G) and edge set E(G). A bijection l : V (G) → {1, 2,...,k} is label function l if opt(l) = min{max(li) : li vertex irregular labeling} ...

All graph in this paper are connected and simple. Let G = (V, E) be a simple graph, where V (G) is vertex set and E(G) is edge set. The local irregularity vertex coloring of G is l : V (G) → {1, 2, · · · , k} and w : V (G) ...

A proper k coloring of graph G such that the neighbors of any vertex v ∈ V (G) where at least min{r, d(v)} different colors is defined an r-dynamic coloring. The minimum k such that graph G has an r-dynamic k coloring is ...