GENERATING TRIANGULAR GRACEFUL TREES FROM CATTERPILLARS BY RECURRING REPEATED ACCESSORY

Abstract

A graph G with a line that is 1-1 g:V(G)→w (w∈W) and the property that the resulting line labels are likewise different is considered to have a graceful labeling. The labels |g(u)-g(w)| are assigned to the line occurrences with the nodes u and w. A graph is considered graceful if it allows for a graceful labeling; the triangular graph of a complete graph is equal to , where an is a positive integer. This study presents an iterative augmentation methodology for combining graceful triangle trees, which is inspired by K. M. Koh's [7] method, which uses well-known graceful trees to obtain larger triangular graceful trees. demonstrate the gracefulness of the repeating repeated added tree , for all x > 0, where is a foundation tree chosen as a caterpillar and An accessory tree identified as a caterpillar is is the term for the tree obtained by combining a replica of  at every node in  for x > 0 that has a degree greater than or equal to two. Consequently, for all repeatedly added caterpillar trees  for x > 0, the triangular elegant tree is accurate.