ISSN:
1522-9602
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract The structural information content (Rashevsky, 1955; Trucco 1956a, b)I g (X) of a graphX is defined as the entropy of the finite probability scheme constructed from the orbits of its automorphism groupG(X). The behavior ofI g on various graph operations—complement, sum, join, cartesian product and composition, is examined. The principal result of the paper is the characterization of a class of graph product operations on whichI g is semi-additive. That is to say, conditions are found for binary operations o and ∇ defined on graphs and groups, respectively, which are sufficient to insure thatI g (X o Y)=I g (X)+I g (Y)−H XY , whereH XY is a certain conditional entropy defined relative to the orbits ofG(X o Y) andG(X) ∇G(Y).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02476948
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