%0 Journal Article
%T A survey of the studies on Gallai and anti-Gallai graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Poovathingal, Agnes
%A Kureethara, Joseph Varghese
%A Deepthy, Dinesan
%D 2021
%\ 06/01/2021
%V 6
%N 1
%P 93-112
%! A survey of the studies on Gallai and anti-Gallai graphs
%K Line graph
%K cograph
%K total graph
%K simplicial complex
%K Gallai-mortal graph
%R 10.22049/cco.2020.26877.1155
%X 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.
%U http://comb-opt.azaruniv.ac.ir/article_14101_3be7cc0e11391991ac4a426d0377a62f.pdf