Odd Triangular Graceful Labeling and Odd Triangular Graceful Number of Special Trees and Some Graphs

Abstract

A flourishing and application-oriented area of research in graph theory is graph labeling. Researchers have been studying graph labeling since the mid-20^th century. A new variation of graceful labeling was introduced in 2001 called triangular graceful labeling which builds on Rosa's 1967  -valuation and Goloumb's graceful labeling. In our recent study, we noticed a variation of triangular graceful labeling introduced in [4] in 2020. It is called odd triangular graceful labeling.  We use throughout the paper  in short form as OTGL . In our study , we establish odd triangular gracefulness of a few classes of tree graphs and found odd triangular graceful number of few families of graphs which we have introduced recently. A graph  with and = is called an OTG graph if there is an one-one function  where  triangular number, (in general ) such that the induced function on  namely  defined by  for every edge  is bijective. The function  is called an OTGL. Here, we establish odd triangular gracefulness of a few classes of tree graphs and found odd triangular graceful number introduced recently by us for few families of graphs.