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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.
This is the third paper in a series of natural language processing in term of knowledge graphs. A word is a basic unit in natural language processing. This is why we study word graphs. Word graphs were already built for prepositions and adwords (including adjectives, adverbs and Chinese quantity words) in two other papers [2], [3]. In this paper, we propose(More)
The concept of a line graph is generalized to that of a path graph. The path graph f,(G) of a graph G is obtained by representing the paths Pk in G by vertices and joining two vertices whenever the corresponding paths f k in G form a path f k + , or a cycle C,. f,-graphs are characterized and investigated on isomorphism and traversability. Trees and(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)
In this paper the results are given of an investigation into concepts from Economics, Organization Theory, Political Science, Psychology and Sociology. The goal of this investigation was to find out whether there is a set of concepts that may be considered to be basic to all these five social sciences. The set of concepts found will be modeled in terms of(More)