Gracefulness of Central Graphs

eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences December 2008 20 3 735 740 jusps-B 1398 article Gracefulness of Central Graphs R. Sattanathan (sreeda.arun@gmail.com) 1 S.Manikandan 2 Reader & Head P.G. & Research, Department of Mathematics, D.G., Vaishnav College, Chennai - 106 (INDIA) Senior Lecturer Department of Mathematics, Sri Sai Ram Engineering College, Chennai - 44 (INDIA) Given a graph G consisting of vertices and edges, a vertex labeling of G is an assignment f of labels to the vertices of G that produces for each edge xy a label depending on the vertex labels f (x) and f (y). A vertex labeling f is called a graceful labeling of a graph G with q edges if f is an injection from the vertices of G to the set {0,1,2,...q} such that when each edge xy is assigned the label |f (x)-f (y)| the resulting edge labels are distinct. A graph G is called graceful if there exists a graceful labeling of G (see figure 1). In this Paper we give some results on Central graphs (The Central Graph C(G) of a graph G is obtained by subdividing each edge of G exactly once and joining all the non-adjacent vertices of G (see figure 2)) and gracefulness of Central graphs of Cycles being investigated.   https://ultraphysicalsciences.org/paper/1398/ Graceful Labeling Central Graphs.