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
Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф ： V（G） U E（G） → （1, 2,…… , k） such that no adjacent vertices receive thesame color and no adjacent edges receive ...Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф ： V（G） U E（G） → （1, 2,…… , k） such that no adjacent vertices receive thesame color and no adjacent edges receive the same color. An/-total coloring of a graph G issaid to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, wehave CФ（u） ≠ CФ（v）, where CФ（u） denotes the set of colors of u and its incident edges. Theminimum number of colors required for an adjacent vertex distinguishing I-total coloring of GG is called the adjacent vertex distinguishing I-total chromatic number, denoted by Xat（G）.In this paper, we characterize the adjacent vertex distinguishing I-total chromatic numberof outerplanar graphs.展开更多
Let G be a maximal outerplane graph and X0(G) the complete chromatic number of G. This paper determines exactly X0(G) for △(G)≠5 and proves 6≤X0.(G)≤7 for △(G) = 5, where △(G) is the maximum degree of vertices o...Let G be a maximal outerplane graph and X0(G) the complete chromatic number of G. This paper determines exactly X0(G) for △(G)≠5 and proves 6≤X0.(G)≤7 for △(G) = 5, where △(G) is the maximum degree of vertices of G.展开更多
Let G be a planar graph without cut vertex, let X_c(G) be the vertex, edge, face-complete chromatic number of G and let p=|V(G)|. This paper proves X_c(G)=Δ(G)+1 if G is an outerplanar graph with Δ(G)≥7, or a high ...Let G be a planar graph without cut vertex, let X_c(G) be the vertex, edge, face-complete chromatic number of G and let p=|V(G)|. This paper proves X_c(G)=Δ(G)+1 if G is an outerplanar graph with Δ(G)≥7, or a high degree planar graph with p≥9 and Δ(G)≥p-2 or a maximal planar graph with Δ(G)≥14.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.
基金Supported by the National Natural Science Foundation of China(61163037,61163054,61363060)
文摘Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф ： V（G） U E（G） → （1, 2,…… , k） such that no adjacent vertices receive thesame color and no adjacent edges receive the same color. An/-total coloring of a graph G issaid to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, wehave CФ（u） ≠ CФ（v）, where CФ（u） denotes the set of colors of u and its incident edges. Theminimum number of colors required for an adjacent vertex distinguishing I-total coloring of GG is called the adjacent vertex distinguishing I-total chromatic number, denoted by Xat（G）.In this paper, we characterize the adjacent vertex distinguishing I-total chromatic numberof outerplanar graphs.
基金Project supported by the Vatural SCience Foundation of LNEC.
文摘Let G be a maximal outerplane graph and X0(G) the complete chromatic number of G. This paper determines exactly X0(G) for △(G)≠5 and proves 6≤X0.(G)≤7 for △(G) = 5, where △(G) is the maximum degree of vertices of G.
基金Project supported by the Natural Science Foundation of the Railway Ministry and Gansu Province.
文摘Let G be a planar graph without cut vertex, let X_c(G) be the vertex, edge, face-complete chromatic number of G and let p=|V(G)|. This paper proves X_c(G)=Δ(G)+1 if G is an outerplanar graph with Δ(G)≥7, or a high degree planar graph with p≥9 and Δ(G)≥p-2 or a maximal planar graph with Δ(G)≥14.
