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Observations Concerning Chordal Graph Polynomials

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  • Allen D. Parks

Abstract

For every graph that is clique equivalent to a connected chordal graph, it is shown that the associated dependence polynomial has a unit root and that the associated clique and independence polynomials have negative unit roots. The dependence polynomial for a graph that is the join of two graphs is also shown to have a unit root when at least one of the two joined graphs is clique equivalent to a connected chordal graph. A condition satisfied by the eigenvalues of graphs that are clique equivalent to connected chordal graphs with clique numbers less than four is identified.

Suggested Citation

  • Allen D. Parks, 2015. "Observations Concerning Chordal Graph Polynomials," International Journal of Sciences, Office ijSciences, vol. 4(01), pages 36-39, January.
    • Handle: RePEc:adm:journl:v:4:y:2015:i:1:p:36-39
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    References listed on IDEAS

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    1. Allen D. Parks, 2013. "Clique Complex Homology: A Combinatorial Invariant for Chordal Graphs," International Journal of Sciences, Office ijSciences, vol. 2(07), pages 96-100, July.
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