Axioms, Vol. 12, Pages 504: On 3-Restricted Edge Connectivity of Replacement Product Graphs

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Axioms, Vol. 12, Pages 504: On 3-Restricted Edge Connectivity of Replacement Product Graphs

Axioms doi: 10.3390/axioms12050504

Authors:
Yilan Cui
Jianping Ou
Saihua Liu

A 3-restricted edge cut is an edge cut of a connected graph that separates this graph into components, each having an order of at least 3. The minimum size of all 3-restricted edge cuts of a graph is called its 3-restricted edge connectivity. This work determines the upper and lower bounds on the 3-restricted edge connectivity of replacement product graphs and presents sufficient conditions for replacement product graphs to be maximally 3-restricted edge connected. As a result, the 3-restricted edge connectivity of replacement product graphs of some special graphs are determined.

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