Supereulerian Indices of Some Classes of Graphs

Researching Supereulerian index of a graph $G$ is NP-hard. In this paper, we consider Supereulerian indices of some classes of graphs, Supereulerian index means the minimum integer $k$ of iterated line graph $L^k\left(G\right)$ of a graph $G$ such that $L^k\left(G\right)$ is Supereulerian. We show that Supereulerian indices of those graphs obtained by replacing every vertex of Petersen graph with $n$ -cycle or a complete graph of order $n$ , or adding $n$ pendant edges to each vertex of Petersen graph are both 1. Concurrently, we show that Supereulerian indices of partial Generalized Petersen graphs are also 1.