On local antimagic chromatic number of spider graphs

An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it Bijection f : E ? {1, … ,|E|} such that for any pair adjacent vertices x and y, f+(x) ? f+(y), where the induced vertex label ?f(e), with e ranging over all edges incident x. The chromatic number G, denoted by ?la(G), minimum distinct labels labelings G. In this paper, we first show d-leg spider has d + 1 ? ?la 2. We then obtain many sufficient conditions both values are attainable. Finally, each 3-leg 4 not legs odd length. No leg lengths 5 found. This provides partial solutions characterization k-pendant trees T ?la(T) k or conjecture almost spiders size q satisfy d(d 1) 2(2q - length at least 2 1.