On bags and bugs

Authors:
Pierre Hansen;Dragan Stevanović
Affiliations:
GERAD, HEC Montréal, 3000 chemin de la Cóte-Sainte-Catherine, Montréal, Canada;Faculty of Science and Mathematics, Višegradska 33, 18000 Niš, Serbia and Montenegro
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

Usual graph classes, such as complete graphs, paths, cycles and stars, frequently appear as extremal graphs in graph theory problems. Here we want to turn the reader's attention to two novel, simply defined, graph classes that appear as extremal graphs in several graph theory problems. We call them bags and bugs. As examples of problems where bags and bugs appear, we show that balanced bugs maximize the index of graphs with fixed number of vertices and diameter =2, while odd bags maximize the index of graphs with fixed number of vertices and radius =3.