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A (k; g)-cage is a k-regular graph of girth g with minimum order. In this work, for all k ≥ 2 and g ≥ 5 odd, we present an upper bound of the order of a (k; g + 1)-cage, which depends on the order of a (k; g)-cage, improving a previous result of Sauer of 1967. We also show that every (k; 11)-cage contains a cycle of length 12, confirming a case of a… (More)

An edge cut W of a connected graph G is a k-restricted edge cut if G−W is disconnected, and every component of G − W has at least k vertices. The k-restricted edge connectivity is defined as the minimum cardinality over all k-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between… (More)

A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1}-semiregular graph if all its vertices have degree either d or d + 1. A smallest {d, d + 1}-semiregular graph G with girth g is said to be a ({d, d + 1}; g)-cage. We show that every… (More)

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