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This paper introduces two kinds of graph polynomials, clique polynomial and independent set polynomial. The paper focuses on expansions of these polynomials. Some open problems are mentioned.
A marked graph is obtained from a graph by giving each point either a positive or a negative sign. Beineke and Harary raised the problem of characterizing consistent marked graphs in which the product of the signs of the points is positive for every cycle. In this paper a characterization is given in terms of fundamental cycles of a cycle basis.
In the theory of knowledge graphs, words are represented by word graphs. Sentences are to be represented by sentence graphs. This is called structural parsing. Under consideration of the semantic and syntactic features of natural language, both semantic and syntactic word graphs are formed, the latter expressing the function of word types like nouns, verbs,… (More)
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to… (More)
©1999 No part of this book may be reproduced in any form by print, photoprint, microfilm or any other means without the prior written permission from the publisher. A publication in coöperation with the Dutch researchgroups SIMULATION and COMPLEX SOCIETAL PROBLEMS of the NOSMO (Dutch Research group on Methodology) Validation of simulation models in the… (More)