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2005•International Journal of Computer MathematicsRequires access

Inverse M-matrices completions of then-chordal graph

Xijuan Guo, Huiping Yao, Fang Cheng

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Abstract

In this paper, the completion problems for chordal graphs and block graphs are discussed using graph theory. Based on the completion theorem for 1-chordal graph, we give the completion theorems for 2-chordal graph and 3-chordal graph, make the completion problem extend to n-chordal graph. We also give the definition of block graph and discuss the completion for 1-chordal block graph, 2-chordal block graph, and 3-chordal block graph. The corresponding algorithms that can be used to get the completions are also presented.

About this research paper

What this paper is about

In this paper, the completion problems for chordal graphs and block graphs are discussed using graph theory. Based on the completion theorem for 1-chordal graph, we give the completion theorems for 2-chordal graph and 3-chordal graph, make the completion problem extend to n-chordal graph. We also give the definition of block graph and discuss the completion for 1-chordal block graph, 2-chordal block graph, and 3-chordal block graph. The corresponding algorithms that can be used to get the completions are also presented.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the completion problems for chordal graphs and block graphs are discussed using graph theory. Based on the completion theorem for 1-chordal graph, we give the completion theorems for 2-chordal graph and 3-chordal graph, make the completion problem extend to n-chordal graph. We also give the definition of block graph and discuss the completion for 1-chordal block graph, 2-chordal block graph, and 3-chordal block graph. The corresponding algorithms that can be used to get the completions are also presented.

Key concepts: Chordal graph, Interval graph, Mathematics, Combinatorics, Block graph, Outerplanar graph, Distance-hereditary graph, Split graph

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