设G=(V,E)是没有孤立顶点的图,并令|V(G)|=n和|E(G)|=m。双射π:V(G)ºE(G)→{1,2,....,n+m}被认为是图G的局部总反魔标记,如果它满足条件:(i。)对于任何边缘uv,ω(u)辛ω(v),其中u和v在V(G)(ii。)对于任何两个相邻的边e和e',ω(e)辛ω(e')(iii.)对于任何边uvεE(G)入射到顶点v,ω(v)辛ω(uv),其中顶点u的权重是,ω(u)=∑eεS(u)π(e),S(u)是边缘的集合,S(u)的每个边缘的一端顶点是u,并且边缘权重是ω(e=uv)=π(u)+π(v)。在本文中,我们引入了局部总反魔术标记(LTAL)和局部总反魔术色数(LTACN)。此外,我们得到图Pn的LTACN,K1,n,Fn和Sn,Understandingthefollows.
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.