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On Spanning and Dominating Circuits in Graphs

Published online by Cambridge University Press:  20 November 2018

L. Lesniak-Foster  and
James E. Williamson
L. Lesniak-Foster
Affiliation:
Louisiana State University, Baton RougeLouisiana 70803 U.S.A.
James E. Williamson
Affiliation:
University of Dubuque, DubuqueIowa 52001 U.S.A.
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Abstract

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A set E of edges of a graph G is said to be a dominating set of edges if every edge of G either belongs to E or is adjacent to an edge of E. If the subgraph 〈E〉 induced by E is a trail T, then T is called a dominating trail of G. Dominating circuits are defined analogously. A sufficient condition is given for a graph to possess a spanning (and thus dominating) circuit and a sufficient condition is given for a graph to possess a spanning (and thus dominating) trail between each pair of distinct vertices. The line graph L(G) of a graph G is defined to be that graph whose vertex set can be put in one-to-one correspondence with the edge set of G in such a way that two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. The existence of dominating trails and circuits is employed to present results on line graphs and second iterated line graphs, respectively.

Keywords

05C35Dominating traildominating circuitspanning trailspanning circuithamiltonian pathhamiltonian cyclehamiltonian graphline graph
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 215 - 220
Copyright
Copyright © Canadian Mathematical Society 1977

References

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