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The connectivity of total graphs

Published online by Cambridge University Press:  17 April 2009

Mehdi Behzad
Mehdi Behzad
Affiliation:
Pahlavi University, Iran, and Western Michigan University, USA.
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Abstract

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We associate with a graph (finite, undirected, without loops and multiple lines) a graph T(G), called the total graph of G. This new graph has the property that a one-to-one correspondence can be established between its points and the elements (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 or incident. The object of this article is to prove the following theorem: If K(G1) = n, n ≥ 1, and λ(G2) = m, m ≥ 1, then K(T(G1)) ≥ n + 2 + [(n - 2)/3], λ(T(G1)) ≥ 2n, K(T(G2)) ≥ m + 1, and λ(T(G2)) ≥ 2m, where k(G) and λ(G) denote the connectivity and line-connectivity of the graph G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 175 - 181
Copyright
Copyright © Australian Mathematical Society 1969

References

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