New Classes of Graceful Unicyclic Graphs

A Cn-unicyclic graph is a unicyclic graph where the cycle has n≥3 vertices. A caterpillar R with spine Pn=v0v1⋯vn−1 is denoted by R(v0v1⋯vn−1). A cycle with a pendant caterpillar is obtained by identifying a vertex of the cycle with a leaf of R(v0v1⋯vn−1) that is adjacent to v0 (or vn−1). In this paper, we investigate the gracefulness of unicyclic graphs with pendant caterpillars at two adjacent vertices of the cycle, and pendant edges at some other vertices of the cycle.