Home > Journals > Active Journals > TAG > Vol. 6 > Iss. 1 (2019)
Publication Date
2018
Abstract
One of the most familiar derived graphs is the line graph. The line graph L(G) of a graph G is that graph whose vertices are the edges of G where two vertices of L(G) are adjacent if the corresponding edges are adjacent in G. Two nontrivial paths P and Q in a graph G are said to be adjacent paths in G if P and Q have exactly one vertex in common and this vertex is an end-vertex of both P and Q. For an integer ℓ ≥ 2, the ℓ -line graph Lℓ (G) of a graph G is the graph whose vertex set is the set of all ℓ -paths (paths of order ℓ) of G where two vertices of Lℓ(G) are adjacent if they are adjacent ℓ-paths in G. Since the 2-line graph is the line graph L(G) for every graph G, this is a generalization of line graphs. In this work, we study planar and outerplanar properties of the 3-line graph of connected graphs and present characterizations of those trees having a planar or outerplanar 3-line graph by means of forbidden subtrees.
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Recommended Citation
Alhulwah, Khawlah H.; Zayed, Mohra; and Zhang, Ping
(2018)
"On the Planarity of Generalized Line Graphs,"
Theory and Applications of Graphs: Vol. 6:
Iss.
1, Article 2.
DOI: 10.20429/tag.2019.060102
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol6/iss1/2
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