Abstract
A generalized adjacency matrix (called “representation matrix”) is defined for a graph: the elements of this matrix are the edge labels. Treating these labels as independent variables, if the determinant is evaluated, the resulting multivariable polynomial parametrizes a graph. This serves as a basis to detect isomorphism, automorphism, subgraph isomorphism, and other graph properties.
Essentially, this paper exhibits the analogy that exists between forms among expressions and isomorphism among graphs. Consequently, many of the graph properties can be inferred from properties, such as symmetry, variable-separable-factorizability, and similarity of forms of the parametrizing polynomial.
It is shown how this formalism can be used for coding a graph. The decoding or reconstruction of a graph from its invariant polynomial code is also described. These will have many practical applications.
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© 1981 Springer-Verlag
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Krishnamurthy, E.V. (1981). A form invariant multivariable polynomial representation of graphs. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092252
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DOI: https://doi.org/10.1007/BFb0092252
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