Valuations of Plane Quartic Graphs

We deal with \((a,d)\)-face antimagic labelings of a certain class of plane quartic graphs. A connected plane graph \(G = (V, E, F)\) is said to be \((a,d)\)-\emph{face antimagic} if there exist positive integers \(a\) and \(d\), and a bijection \(g : E(G) \rightarrow \{1,2,…,|E(G)|\}\) such that the induced mapping \(\varphi_g : F(G) \rightarrow {N}\), defined by \(\varphi_g(f) = \sum\{g(e): e \in E(G) \text{ adjacent to face } f\}\), is injective and \(\varphi_g(F) = \{a,a+d,…,a+ (|F(G)| – 1)d\}\).