Local total anti-magic chromatic number of graphs

Let [Formula: see text] be a graph without isolated vertices and let [Formula: see text] and [Formula: see text]. A bijection [Formula: see text] is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, [Formula: see text] , where u and v in [Formula: see text] (ii.) for any two adjacent edges e and [Formula: see text] , [Formula: see text] (iii.) for any edge [Formula: see text] is incident to the vertex v, [Formula: see text] , where weight of vertex u is, [Formula: see text] , [Formula: see text] is the set of edges with every edge of [Formula: see text] one end vertex is u and an edge weight is [Formula: see text]. 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 [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text].