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Total Graphs and Traversability

Published online by Cambridge University Press:  20 January 2009

Mehdi Behzad
Affiliation:
Wayne State University, AND Pahlavi University, Iran,
Gary Chartrand
Affiliation:
The University of Michigan, and Western Michigan University
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With every graph G (finite and undirected with no loops or multiple lines) there is associated a graph L(G), called the line-graph of G, whose points correspond in a one-to-one manner with the lines of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of Gare adjacent. This concept was originated by Whitney (3). In a similar way one can associate with G another graph which we call its total graph and denote by T(G). This new graph has the property that a one-to-one correspondence can be established between its points and the elements (the set of points and lines) of G such that two points of T(G) are adjacent if and only if the corresponding elements of G are adjacent (if both elements are points or both are lines) or theyare incident

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Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1966