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Location of zeros of Wiener and distance polynomials.

Dehmer M, Ilić A - PLoS ONE (2012)

Bottom Line: A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated.In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated.Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

View Article: PubMed Central - PubMed

Affiliation: Institute for Bioinformatics and Translational Research, UMIT - The Health and Lifesciences University Hall/Tyrol, Hall in Tyrol, Austria. matthias.dehmer@umit.at

ABSTRACT
The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

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A graph .
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pone-0028328-g004: A graph .

Mentions: Note that a tree is a connected graph without cycles, or a connected graph with exactly edges. A unicyclic graph is a connected graph with exactly one cycle, or a connected graph with exactly edges. Analogously, a bicyclic graph is a connected graph with exactly two cycles, or a connected graph with exactly edges. These simple types of graphs have often been used in mathematical chemistry and as underlying structure of chemical compounds. From these characterizations, the most important structural properties of our graph classes are known. Some characteristic graphs from the graph classes , , and are depicted in Figure (1)–(4).


Location of zeros of Wiener and distance polynomials.

Dehmer M, Ilić A - PLoS ONE (2012)

A graph .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3306308&req=5

pone-0028328-g004: A graph .
Mentions: Note that a tree is a connected graph without cycles, or a connected graph with exactly edges. A unicyclic graph is a connected graph with exactly one cycle, or a connected graph with exactly edges. Analogously, a bicyclic graph is a connected graph with exactly two cycles, or a connected graph with exactly edges. These simple types of graphs have often been used in mathematical chemistry and as underlying structure of chemical compounds. From these characterizations, the most important structural properties of our graph classes are known. Some characteristic graphs from the graph classes , , and are depicted in Figure (1)–(4).

Bottom Line: A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated.In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated.Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

View Article: PubMed Central - PubMed

Affiliation: Institute for Bioinformatics and Translational Research, UMIT - The Health and Lifesciences University Hall/Tyrol, Hall in Tyrol, Austria. matthias.dehmer@umit.at

ABSTRACT
The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

Show MeSH