The local vertex anti-magic coloring for certain graph operations

This work proves the local vertex anti -magic coloring of even regular circulant bipartite graphs C ( m ; L ). Let G be either K , or K , - F , F is a 1 -factor. Also, we discover the local vertex antimagic coloring for union of bipartite graphs; join graphs G boolean OR H , where H is an element of { , K , C , K , }; and the upper bound of corona product G circle dot . It was a problem Lau and Shiu (2023) [1] that: For any G 1 and G 2 , determine ea ( G 1 x G 2 ). We give partial answer to this problem by proving the followings: 1. ea ( C 2 m x C 2 n ); 2. ea ( C 2 m +1 x C 2 n +2 ); and 3. ea ( P 3 x H ), where H is an element of { K , K m,m }.