Abstract
The structural information contentI g (X) of a graphX was treated in detail in three previous papers (Mowshowitz 1968a, 1968b, 1968c). Those investigations ofI g point up the desirability of defining and examining other entropy-like measures on graphs. To this end the chromatic information contentI c (X) of a graphX is defined as the minimum entropy over all finite probability schemes constructed from chromatic decompositions having rank equal to the chromatic number ofX. Graph-theoretic results concerning chromatic number are used to establish basic properties ofI c on arbitrary graphs. Moreover, the behavior ofI c on certain special classes of graphs is examined. The peculiar structural characteristics of a graph on which the respective behaviors of the entropy-like measuresI c andI g depend are also discussed.
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Literature
Hedetniemi, S. 1966. “Homomorphisms of Graphs and Automata.” Technical Report 03105-44-T, Office of Research Administration, The University of Michigan.
Mowshowitz, A. 1968a. “Entropy and the Complexity of Graphs: I. An Index of the Relative Complexity of a Graph.”Bull. Math. Biophysics,30, 175–204.
— 1968b. “Entropy and the Complexity of Graphs: II. The Information Content of Digraphs and Infinite Graphs”.Ibid.,,30, 225–240.
— 1968c. “Entropy and the Complexity of Graphs: III. Graphs with Prescribed Information Content.”Ibid.,,30, 387–414.
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Mowshowitz, A. Entropy and the complexity of graphs: IV. Entropy measures and graphical structure. Bulletin of Mathematical Biophysics 30, 533–546 (1968). https://doi.org/10.1007/BF02476673
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DOI: https://doi.org/10.1007/BF02476673