Abstract
In this last chapter of Part I, the focus is on local relationships between elements of a line graph. Among these are discrete analogues of the geometric concepts of diameter, radius, and center. Some of the results involve connections for these quantities between graphs and their line graphs, and what happens to their values in iterated line graphs. The center of a graph is also defined in a natural way, and some intriguing results on the center of a line graph are described. The other topic is in response to a question about partially ordered sets: Which line graphs can their edges oriented so that the result is a transitive ordering? The answer can be given in terms of forbidden subgraphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Knor, L'. Niepel, L'. Šoltés, Centers in iterated line graphs. Acta Math. Univ. Comenianae 61, 237–241 (1992)
M. Knor, L'. Niepel, L'. Šoltés, Centers in line graphs. Math. Slovaka 43, 11–20 (1993)
L'. Niepel, M. Knor, L'. Šoltés, Distances in iterated line graphs. Ars Combin. 43, 193–202 (1996)
M. Petkovšek, Comparability line graphs, in Graph Theory (Novi Sad, 1983). University of Novi Sad (1984), pp. 231–244
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Beineke, L.W., Bagga, J.S. (2021). Distance and Transitivity in Line Graphs. In: Line Graphs and Line Digraphs. Developments in Mathematics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-030-81386-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-81386-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81384-0
Online ISBN: 978-3-030-81386-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)