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The M¨obius ladder of size 6 is the graph Γ6∗ discussed in Sect. 3 which contains no cubic crackers. References 1. : The characteristic polynomial does not uniquely determine the topology of a molecule. J. Chem. Doc. 11, 258–259 (1971) 2. : Recent progress in combinatorics. T. ) Proceedings of the Third Waterloo Conference on Combinatorics, May 1968. Academic, New York (1969) 3. : Inductive classes of graphs. In: Proceedings of the Sixth Yugoslav Seminar on Graph Theory, Dubrovnik, 1985, pp. 43–56 (1986) 4.
An Atlas of Graphs, p. 263. Oxford University Press, Oxford (1998) 19. : Constructive enumeration of graphs. D. thesis, University of Western Australia (1987) Chapter 2 Inherited Properties of Descendants Abstract Given the results of Chap. 1 that every descendant may be constructed from a complete family of ancestor genes, we now investigate how the properties of the descendant correspond to the properties of those genes. In particular we consider the properties of Hamiltonicity, bipartiteness and planarity.
Then, we can obtain ΓD from the type 3 breeding operation B3 (Γ1 , Γ2 , v7 , v8 , v1 , v3 , v5 , v2 , v4 , v6 ). This situation can be seen in Fig. 22. Fig. 3 Note that any 3-cracker can be introduced via a type 3 breeding operation, and therefore all 3-crackers are irreducible. 11. We refer to a family of genes that can, through a series of breeding and parthenogenic operations, be used to produce a descendant ΓD as a complete family of ancestor genes of ΓD , and we say that ΓD possesses this complete family of ancestor genes.