Open Access
December 2018 Edge connectivity and restricted edge connectivity of cartesian product of graphs
Maho Yokota
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SUT J. Math. 54(2): 161-171 (December 2018). DOI: 10.55937/sut/1547570578


An edge cutset EE(G) of a graph G is called a restricted edge cutset if every component of GE has order at least 2. We let λ(G) denote the minimum cardinality of a restricted edge cutset of G, and let δ(G) denote the minimum of degG(x)+degG(y)2 as x and y range over all adjacent vertices of G. We let λ(G) and δ(G) denote the edge connectivity and the minimum degree of G, respectively. Among other results, we show that if G1 and G2 are graphs such that λ(Gi)=δ(Gi)2 and λ(Gi)=δ(Gi)2 for each i=1,2, then λ(G1G2)=δ(G1G2)=min{δ(G1)+2δ(G2),δ(G2)+2δ(G1)}, where G1G2 denotes the cartesian product of G1 and G2.


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Maho Yokota. "Edge connectivity and restricted edge connectivity of cartesian product of graphs." SUT J. Math. 54 (2) 161 - 171, December 2018.


Received: 14 October 2018; Revised: 26 November 2018; Published: December 2018
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1547570578

Primary: 05C40

Keywords: Cartesian product , edge connectivity

Rights: Copyright © 2018 Tokyo University of Science

Vol.54 • No. 2 • December 2018
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