2022/12/10 by Deepthi, Nayana Shibu
#05C78 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2212.05329
Let G be a finite simple undirected (p,q)-graph, with vertex set V(G) and edge set E(G) such that p=|V(G)| and q=|E(G)|. A super edge-magic total labeling f of G is a bijection f\colon V(G)∪ E(G)\longrightarrow \1,2,… , p+q\ such that for all edges u v∈ E(G), f(u)+f(v)+f(u v)=c(f), where c(f) is called a magic constant, and f(V(G))=\1,… , p\. The minimum of all c(f), where the minimum is taken over all the super edge-magic total labelings f of G, is defined to be the super edge-magic total strength of the graph G. In this article, we work on certain classes of unicyclic graphs and provide shreds of evidence to conjecture that the super edge-magic total strength of a certain family of unicyclic (p,q)-graphs is equal to 2q+(n+3)/(2).