Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 6 1 2021 06 01 A survey of the studies on Gallai and anti-Gallai graphs 93 112 14101 10.22049/cco.2020.26877.1155 EN Agnes Poovathingal Christ University, Bangalore, India Joseph Varghese Kureethara Christ University, Bangalore, India Dinesan Deepthy Department of Mathematics, GITAM University, Bangalore, India Journal Article 2020 07 17 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. https://comb-opt.azaruniv.ac.ir/article_14101_3be7cc0e11391991ac4a426d0377a62f.pdf