A total k-coloring of a graph GG is a mapping ϕ: V (G) ∪ E (G) → k={1, 2, ..., k\} ϕ: V (G)∪ E
(G)→ k= 1, 2,…, k such that any two adjacent or incident elements in V (G) ∪ E (G) V (G)∪ E …

A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the
set [h]={1, 2,…, h}. Let w (u) denote the sum of the color on a vertex u and colors on all the …

Given a simple graph G, a proper total-k-coloring ϕ: V (G)∪ E (G)→{1, 2,…, k} is called
neighbor sum distinguishing if S ϕ (u)≠ S ϕ (v) for any two adjacent vertices u, v∈ V (G) …

Abstract Let G=(V, E) be a graph and φ be a total coloring of G by using the color set {1, 2,...,
k}. Let f (ν) denote the sum of the color of the vertex ν and the colors of all incident edges of …

Let c be a proper total coloring of a graph G=(V, E) with integers 1, 2,…, k. For any vertex v∈
V (G), let∑ c (v) denote the sum of colors of the edges incident with v and the color of v. If for …

A total-k-coloring of a graph G is a mapping c: V (G) ∪ E (G) → {1, 2,\dots, k\} c: V (G)∪ E
(G)→ 1, 2,⋯, k such that any two adjacent or incident elements in V (G) ∪ E (G) V (G)∪ E (G) …

Halal cuisine is an essential requirement for every Muslim. However, the number of halal-
certified products are less than number of non-halal-certified products. Therefore, we …

Abstract Let G=(V, E) G=(V, E) be a graph and ϕ: V ∪ E → {1, 2, ..., k\} ϕ: V∪ E→ 1, 2,…, k
be a total coloring of G. Let C (v) denote the set of the color of vertex v and the colors of the …

Abstract A (proper) total [k]-coloring of a graph G is a mapping ϕ: V (G)∪ E (G)→[k]={1, 2,…,
k} such that any two adjacent elements in V (G)∪ E (G) receive different colors. Let f (v) …

Abstract A (proper) total-k-coloring ϕ: V (G)∪ E (G)→{1, 2,…, k} is called adjacent vertex
distinguishing if C ϕ (u)≠ C ϕ (v) for each edge uv∈ E (G), where C ϕ (u) is the set of the …