Super restricted edge connected Cartesian product graphs

Authors:
Juan Liu;Xing Chen;Jixiang Meng
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China and College of Maths-physics and Information Sciences, Xinjiang Normal University, Urumqi, Xinjia ...;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China
Venue:
Information Processing Letters
Year:
2009

Citing 7
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Abstract

An edge-cut F of a connected graph G is called a restricted edge-cut if G-F contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity @l^'(G) of G. A graph G is said to be @l^'-optimal if @l^'(G)=@x(G), where @x(G) is the minimum edge-degree of G. A graph is said to be super-@l^' if every minimum restricted edge-cut isolates an edge. This article gives a sufficient condition for Cartesian product graphs to be super-@l^'. Using this result, certain classes of networks which are recursively defined by the Cartesian product can be simply shown to be super-@l^'.