a survey of the studies on gallai and anti-gallai graphs

the gallai graph and the anti-gallai graph of a graph g are edge disjoint spanning subgraphs of the line graph l(g). the vertices in the gallai graph are adjacent if two of the end vertices of the corresponding edges in g coincide and the other two end vertices are nonadjacent in g. the anti-gallai graph of g is the complement of its gallai graph in l(g). attributed to gallai (1967), the study of these graphs got prominence with the work of sun (1991) and le (1996). this is a survey of the studies conducted so far on gallai and anti-gallai of graphs and their associated properties.