On an edge partition and root graphs of some classes of line graphs
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 classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the G...
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| Main Authors: | , |
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| Format: | EJournal Article |
| Published: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2017-04-10.
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| Subjects: | |
| Online Access: | Get Fulltext |
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| Summary: | 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 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 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. |
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| Item Description: | https://www.ejgta.org/index.php/ejgta/article/view/263 |