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Pm-saturated graphs with minimum size

100%

Dudek A. , Wojda A. P.

2004

tom Vol. 24, no. 1

43-55

By Pm we denote a path of order m. A graph G is said to be Pm - saturated if G has no subgraph isomorphic to Pm and adding any new edge to G creates a Pm in G. In 1986 L. Kaszonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n; Pm) of Pm-saturated graph and characterize the graphs of Sat(n; Pm) - the set of Pm-saturated graphs of minimum size. They have solved this problem for [formula].

Networks with Extremal Closeness

100%

Rupnik Poklukar D. , Žerovnik J.

tom Vol. 167, nr 3

219--234

Closeness is a measure of centrality, an important feature of communication and social networks. Extremal networks among all graphs and among several subclasses of graphs including trees and cacti are given. In addition, maximal graphs among cacti with fixed number of cycles and among cacti with given number of cut edges are provided.