Adjoint polynomials of bridgepath and bridgecycle graphs and Chebyshev polynomials

Toufik Mansour

doi:10.1016/j.disc.2011.04.022

Adjoint polynomials of bridgepath and bridgecycle graphs and Chebyshev polynomials

Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial Σ_k=1ⁿα_k(G)x(x-1) ⋯(x-k+1) of degree n, where α_k(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be Σ_k=1ⁿα_k(Ḡ)x ^k, where Ḡ is the complement of G. We find explicit formulas for the adjoint polynomials of the bridgepath and bridgecycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.

Original language	English
Pages (from-to)	1778-1785
Number of pages	8
Journal	Discrete Mathematics
Volume	311
Issue number	16
DOIs	https://doi.org/10.1016/j.disc.2011.04.022
State	Published - 28 Aug 2011

Keywords

Adjoint polynomial
Bridgegraph
Chebyshev polynomial

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.04.022

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title = "Adjoint polynomials of bridgepath and bridgecycle graphs and Chebyshev polynomials",

abstract = "The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial Σk=1nαk(G)x(x-1) ⋯(x-k+1) of degree n, where αk(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be Σk=1nαk(Ḡ)x k, where Ḡ is the complement of G. We find explicit formulas for the adjoint polynomials of the bridgepath and bridgecycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.",

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N2 - The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial Σk=1nαk(G)x(x-1) ⋯(x-k+1) of degree n, where αk(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be Σk=1nαk(Ḡ)x k, where Ḡ is the complement of G. We find explicit formulas for the adjoint polynomials of the bridgepath and bridgecycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.

AB - The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial Σk=1nαk(G)x(x-1) ⋯(x-k+1) of degree n, where αk(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be Σk=1nαk(Ḡ)x k, where Ḡ is the complement of G. We find explicit formulas for the adjoint polynomials of the bridgepath and bridgecycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.

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KW - Bridgegraph

KW - Chebyshev polynomial

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EP - 1785

JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Adjoint polynomials of bridgepath and bridgecycle graphs and Chebyshev polynomials

Abstract

Keywords

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