✦ LIBER ✦

The connectivities of line and total graphs

✍ Scribed by Douglas Bauer; Ralph Tindell

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 371 KB
Volume: 6
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190060214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Sharp lower bounds for the point connectivity and line connectivity of the line graph L(G) and the total graph T(G) of a graph G are determined. The lower bounds are expressed in terms of the point connectivity k, line connectivity λ, and minimum degree δ of G. It is also shown that 2λ is an upper bound for k(T(G)) and that λ(T(G))= 2δ = δ(T(G)). In each case the realizable values beyond the lower bound are determined.

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