Abstract
Let G = (V, E) be a graph without isolated vertices and let |V(G)| = n and |E(G)| = m. A bijection π:V(G) ∪ E(G) → {1, 2, ...., n + m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u) ≠ ω(v), where u and v in V(G) (ii.) for any two adjacent edges e and e', ω(e) ≠ ω(e') (iii.) for any edge uv ∈ E(G) is incident to the vertex v, ω(v) ≠ ω(uv), where weight of vertex u is, ω(u) = ∑e∈S(u)π(e), S(u) is the set of edges with every edge of S(u) one end vertex is u and an edge weight is ω(e = uv) = π(u) + π(v). In this paper, we have introduced a local total anti-magic labeling (LTAL) and the local total anti-magic chromatic number (LTACN). Also, we obtain the LTACN for the graphs Pn, K1,n, Fn and Sn,n.