Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 5, Number 4 (2001), 789-801.
RECOGNIZING HINGE-FREE LINE GRAPHS AND TOTAL GRAPHS
In this paper, we characterize line graphs and total graphs that are hinge-free, i.e., there is no triple of vertices $x,y,z$ such that the distance between $y$ and $z$ increases after $x$ is removed. Based on our characterizations, we show that given a graph $G$ with $n$ vertices and $m$ edges, determining its line graph and total graph to be hinge-free can be solved in O($n+m$) time. Moreover, characterizations of hinge-free iterated line graphs and total graphs are also discussed.
Taiwanese J. Math., Volume 5, Number 4 (2001), 789-801.
First available in Project Euclid: 20 July 2017
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Chang, Jou-Ming; Ho, Chin-Wen. RECOGNIZING HINGE-FREE LINE GRAPHS AND TOTAL GRAPHS. Taiwanese J. Math. 5 (2001), no. 4, 789--801. doi:10.11650/twjm/1500574996. https://projecteuclid.org/euclid.twjm/1500574996