Let x（G^2） denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1 y3, y3y5, y5y1 to a 6-cycle y1y2…y6y1. In this paper...Let x（G^2） denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1 y3, y3y5, y5y1 to a 6-cycle y1y2…y6y1. In this paper, it is proved that △ ＋ 1 ≤ x（G^2） ≤△ ＋ 2, and x（G^2） = A ＋ 2 if and only if G is Q, where A represents the maximum degree of G.展开更多
Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means ...Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means of the compressing graph and group theory method are given first. Then the relationships between Catalan numbers and the numbers of labeled and unlabeled maximal outerplanar graphs are presented. The computed results verified these formulas.展开更多
The spectral radius is an important parameter of a graph related to networks. A method for estimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of a Hamiltonian planar g...The spectral radius is an important parameter of a graph related to networks. A method for estimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of a Hamiltonian planar graph of order n≥4 is less than or equal to 2+3n-11 and the spectral radius of the outerplanar graph of order n≥6 is less than or equal to 22+n-5, which are improvements over previous results. A direction for further study is then suggested.展开更多
文摘Let x（G^2） denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1 y3, y3y5, y5y1 to a 6-cycle y1y2…y6y1. In this paper, it is proved that △ ＋ 1 ≤ x（G^2） ≤△ ＋ 2, and x（G^2） = A ＋ 2 if and only if G is Q, where A represents the maximum degree of G.
文摘Catalan number is an important class of combinatorial numbers. The maximal outerplanar graphs are important in graph theory. In this paper some formulas to enumerate the numbers of maximal outerplanar graphs by means of the compressing graph and group theory method are given first. Then the relationships between Catalan numbers and the numbers of labeled and unlabeled maximal outerplanar graphs are presented. The computed results verified these formulas.
基金the National Natural Science Foundationof China (No.196 710 5 0 )
文摘The spectral radius is an important parameter of a graph related to networks. A method for estimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of a Hamiltonian planar graph of order n≥4 is less than or equal to 2+3n-11 and the spectral radius of the outerplanar graph of order n≥6 is less than or equal to 22+n-5, which are improvements over previous results. A direction for further study is then suggested.
