(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G be a graph with n vertices and m edges without isolated vertices. A local total antimagic labeling of a graph G is defined as there is a bijection f:V(G)E(G)→ { 1,2,...,n+m}, with for any two adjacent vertices u and v with weights w(u) eq w(v), for any two adjacent edges e_1=uv and e_2=vw with their weights w(e) eq w(e’) and any vertex x incident to an edge e=xy with their weights w(x) eq w(xy). The vertex weight w(u) is defined by w(u)=_eE(u) f(e), where E(u) is the set of edges incident to u. The edge weight w(e=pq) is defined by w(e=pq)=f(p)+f(q). The local total antimagic chromatic number is the minimum number of colors taken over all induced by local total antimagic colorings (labelings) of G, which is denoted by χ_lt(G). In this paper, we determine the local total antimagic chromatic number for the disjoint union of star graphs.