The eavesdropping number of a graph

Stuart, Jeffrey L.. "The eavesdropping number of a graph." Czechoslovak Mathematical Journal 59.3 (2009): 623-636. <http://eudml.org/doc/37947>.

@article{Stuart2009,
abstract = {Let $G$ be a connected, undirected graph without loops and without multiple edges. For a pair of distinct vertices $u$ and $v$, a minimum $\lbrace u,v\rbrace $-separating set is a smallest set of edges in $G$ whose removal disconnects $u$ and $v$. The edge connectivity of $G$, denoted $\lambda (G)$, is defined to be the minimum cardinality of a minimum $\lbrace u,v\rbrace $-separating set as $u$ and $v$ range over all pairs of distinct vertices in $G$. We introduce and investigate the eavesdropping number, denoted $\varepsilon (G)$, which is defined to be the maximum cardinality of a minimum $\lbrace u,v\rbrace $-separating set as $u$ and $v$ range over all pairs of distinct vertices in $G$. Results are presented for regular graphs and maximally locally connected graphs, as well as for a number of common families of graphs.},
author = {Stuart, Jeffrey L.},
journal = {Czechoslovak Mathematical Journal},
keywords = {eavesdropping number; edge connectivity; maximally locally connected; cartesian product; vertex disjoint paths; eavesdropping number; edge connectivity; maximally locally connected; Cartesian product; vertex disjoint paths},
language = {eng},
number = {3},
pages = {623-636},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The eavesdropping number of a graph},
url = {http://eudml.org/doc/37947},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Stuart, Jeffrey L.
TI - The eavesdropping number of a graph
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 623
EP - 636
AB - Let $G$ be a connected, undirected graph without loops and without multiple edges. For a pair of distinct vertices $u$ and $v$, a minimum $\lbrace u,v\rbrace $-separating set is a smallest set of edges in $G$ whose removal disconnects $u$ and $v$. The edge connectivity of $G$, denoted $\lambda (G)$, is defined to be the minimum cardinality of a minimum $\lbrace u,v\rbrace $-separating set as $u$ and $v$ range over all pairs of distinct vertices in $G$. We introduce and investigate the eavesdropping number, denoted $\varepsilon (G)$, which is defined to be the maximum cardinality of a minimum $\lbrace u,v\rbrace $-separating set as $u$ and $v$ range over all pairs of distinct vertices in $G$. Results are presented for regular graphs and maximally locally connected graphs, as well as for a number of common families of graphs.
LA - eng
KW - eavesdropping number; edge connectivity; maximally locally connected; cartesian product; vertex disjoint paths; eavesdropping number; edge connectivity; maximally locally connected; Cartesian product; vertex disjoint paths
UR - http://eudml.org/doc/37947
ER -