Dominance Graph of Binary Words

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SHAVEISI FARZAD; Nasouri Soheila

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ISSN: 2588-4824

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2019 | Volume:9 | Issue:2 Page(s): 191-205

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Title

Dominance Graph of Binary Words

Author(s)

SHAVEISI FARZAD | Nasouri Soheila | Issue Writer Certificate

Keywords

Dominance graph of BinaryQ1

wordsQ2

DiameterQ1

GirthQ2

Radius ChromaticQ1

number Independence numberQ1

Abstract

The dominance graph of the binary words, which is denoted by (Γ _n ) ⃗ , is a directed graph whose vertex set is the set of all binary words of length n. Setting B_1 (w)={1≤ i≤ n┤ | w_i=1}, for every vertex 〖 w_1 w_2… w〗 _n, we join two vertices v and w by an arc if B_1 (w) is contained in B_1 (v). In this paper, we study some graphical parameters of this graph. For example, after computing the distance of every two vertices and the eccentricity of any vertex, it is proved that the Diameter and the radius of the underlying graph of (Γ _n ) ⃗ equals 3 and 2, respectively. Also, it is proved that this graph has 〖 3〗 ^n-3(2^n-1) edges. Then we prove that both of the clique nmber and the chromatic number of the Dominance graph of Binary words of length n are n-1. Among other results, it is shown that the edge chromatic number and the maximum degree of vertices are equal to 2^(n-1)-2. Finally, by a combinatorial method, the independence number of this graph is determined, too.

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APA: Copy

SHAVEISI, FARZAD, & Nasouri, Soheila. (2019). Dominance Graph of Binary Words. ADVANCES IN MATHEMATICAL MODELING, 9(2 ), 191-205. SID. https://sid.ir/paper/243881/en

Vancouver: Copy

SHAVEISI FARZAD, Nasouri Soheila. Dominance Graph of Binary Words. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2019;9(2 ):191-205. Available from: https://sid.ir/paper/243881/en

IEEE: Copy

FARZAD SHAVEISI, and Soheila Nasouri, “Dominance Graph of Binary Words,” ADVANCES IN MATHEMATICAL MODELING, vol. 9, no. 2 , pp. 191–205, 2019, [Online]. Available: https://sid.ir/paper/243881/en

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