## Taiwanese Journal of Mathematics

### RECOGNIZING HINGE-FREE LINE GRAPHS AND TOTAL GRAPHS

#### Abstract

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.

#### Article information

Source
Taiwanese J. Math., Volume 5, Number 4 (2001), 789-801.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574996

Digital Object Identifier
doi:10.11650/twjm/1500574996

Mathematical Reviews number (MathSciNet)
MR1870048

Zentralblatt MATH identifier
0995.05127

#### Citation

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