Connectivity of generalized prisms over G
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
Convex hulls of dense balanced graphs
Journal of Computational and Applied Mathematics - Special issue on asymptotic methods in analysis and combinatorics
Fractional arboricity, strength, and principal partitions in graphs and matroids
Discrete Applied Mathematics - Special issue: graphs in electrical engineering, discrete algorithms and complexity
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
Algorithms and Models for the Web-Graph
Characterization of removable elements with respect to having k disjoint bases in a matroid
Discrete Applied Mathematics
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There are several density functions for graphs which have found use in various applications. In this paper, we examine two of them, the first being given by b(G)=|E(G)|/|V(G)|, and the other being given by g(G)=|E(G)|/(|V(G)|-@w(G)), where @w(G) denotes the number of components of G. Graphs for which b(H)@?b(G) for all subgraphs H of G are called balanced graphs, and graphs for which g(H)@?g(G) for all subgraphs H of G are called 1-balanced graphs (also sometimes called strongly balanced or uniformly dense in the literature). Although the functions b and g are very similar, they distinguish classes of graphs sufficiently differently that b(G) is useful in studying random graphs, g(G) has been useful in designing networks with reduced vulnerability to attack and in studying the World Wide Web, and a similar function is useful in the study of rigidity. First we give a new characterization of balanced graphs. Then we introduce a graph construction which generalizes the Cartesian product of graphs to produce what we call a generalized Cartesian product. We show that generalized Cartesian product derived from a tree and 1-balanced graphs are 1-balanced, and we use this to prove that the generalized Cartesian products derived from 1-balanced graphs are 1-balanced.