Some Results on Regularable Graphs

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 label all its edges with 1's.This problem is exactly the reverse problem of the irregular assignment of graphs and can be viewed as another version of magic labelling and M-cordial labelling of graphs.Particularly we have shown that a graph can never be regularable, can be regularable with only = 0 with the use of negative integers as the edge labels or with R > 0. General characterization of graphs appear to be quite difficult graph labelling problem. In this work we have also investigated regularability of a class of graphs such as wheels, fans, grids etc