On friendly index sets of 2-regular graphs Original Research Article

Let image be a graph with vertex set image and edge set image, and let image be an abelian group. A labeling image induces an edge labeling image defined by image. For image, let image and image. A labeling image is said to be image-friendly if image for all image, and image-cordial if we also have image for all image. When image, the friendly index set of the graph image is defined as image. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order image is cordial if and only if image (mod 4).