3 problems

Let $G$ be a graph, and let $K_2$ denote the complete graph with two vertices. A graph is 1-planar if it has a drawing in the plane in which every edge is crossed by at most one ot…

Let $G$ and $H$ be graphs, let $G[H]$ be their lexicographic product, and let $\chi_{la}$ and $\chi$ denote the local antimagic chromatic number and chromatic number, respectively.…

Let $G$ and $H$ be disjoint non-null graphs. Write $G[H]$ for their lexicographic product, and let $\chi_{la}(G)$ denote the local antimagic chromatic number and $\chi(G)$ the chro…