The well-known conjecture of Ringel-Kotzig or better known graceful tree conjecture has entered to its fourth decade. As today there exits no serious attempts toward its resolution, so it is worthwhile to revisit some old concepts. In this paper we have investigated small ( i.e., trees with...

A directed graph with vertices and e arcs, no self-loops, and no more than one arc directed from any vertex to any vertex , is numbered by assigning to each vertex a distinct element from the set = {1, 2,..., +1}. An arc (, ) from vertex to vertex is numbered (, )= () − () mod ( + 1), where ()...

The labeling problem considered for this is called face-labeling of the maximal planar or triangular planar graphs in connection with the notion of the . Several triangular planar and maximal planar graphs such as the wheels, the fans etc. have been considered. The face-labeling of maximal...

In this paper we study packing the sequence of gracefully labelled trees , , …, with 1, 2, .., − 1 edges into the complete graph . It is shown that if ∈ {, } where and are, respectively, a star tree and a path on vertices then the packing is possible

A graph is called regularable if it is possible to label its edges with integers so that the sum of the integers assigned to the edges incident to the vertices are all same, say equal to . Clearly if the given graph is regular of degree then there is no need to find an edge-assignment; simply...

A tree is said to be -magic if there exits a super magic labeling such that then the vertices of is partioned into three color classes , , so that the vertex labels in ∈ {1,2,3} are all consecutive labels. In this paper we have given -magic labeling of a class of trees with diameter four that...

A cubic tree is a tree in which except for its pendant vertices all of its internal vertices are of degree three. We have explored the embedding of the cubic trees into rectangular grid of minimum size such that the edges are either horizontal or vertical segment. We have also given necessary...

The recent efforts of Hrnciar and Haviar which is based on the case analysis and simple transformations on the selected gracefully labeled starter tree results in that "all trees of diameter five are graceful". The resulting graceful labeling often are of the type "spiral canonic" or similar...