On an edge partition and root graphs of some classes of line graphs

On an edge partition and root graphs of some classes of line graphs

Blog Article

The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$.In this paper we find some structural relations between these graph Construction Set Toys classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and L-Arginine anti-Gallai graphs of $G$.Based on this, an optimal algorithm to find the root graph of a line graph is obtained.Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.