# Search results for: Xueliang Li

Journal of Combinatorial Optimization > 2019 > 38 > 1 > 268-277

*G*, where

*G*is called the underlying graph of $$G^\sigma $$ G σ . Let $$S(G^\sigma )$$ S ( G σ ) denote the skew-adjacency matrix of $$G^\sigma $$ G σ and $$\alpha (G)$$ α ( G ) be the independence number of

*G*. The rank of $$S(G^\sigma )$$ S ( G...

Graphs and Combinatorics > 2018 > 34 > 6 > 1553-1563

*G*is

*conflict-free connected*if every two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The

*conflict-free connection number*of a connected graph

*G*, denoted by

*cfc*(

*G*), is the smallest number of colors needed in order to make

*G*conflict-free connected. For a graph

*G*, let

*C*(

*G*) be the subgraph of

*G*induced by its set of cut-edges...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 458-471

*T*in an edge-colored graph is called a

*proper tree*if no two adjacent edges of

*T*receive the same color. Let

*G*be a connected graph of order

*n*and

*k*be an integer with $$2\le k \le n$$ 2≤k≤n . For $$S\subseteq V(G)$$ S⊆V(G) and $$|S| \ge 2$$ |S|≥2 , an

*S*-

*tree*is a tree containing the vertices of

*S*in

*G*. A set $$\{T_1,T_2,\ldots ,T_\ell \}$$ {T1,T2,…,Tℓ} of

*S*-trees is called

*internally disjoint*...

Journal of Combinatorial Optimization > 2018 > 35 > 4 > 1300-1311

*vertex-monochromatic path*if its internal vertices have the same color. A vertex-coloring of a graph is a

*monochromatic vertex-connection coloring*(

*MVC-coloring*for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph

*G*, the

*monochromatic vertex-connection number*, denoted by

*mvc*(

*G*), is defined to be...

Results in Mathematics > 2017 > 72 > 4 > 2079-2100

*total-colored*if all the edges and the vertices of the graph are colored. A total-colored graph is

*total-rainbow connected*if any two vertices of the graph are connected by a path whose edges and internal vertices have distinct colors. For a connected graph

*G*, the

*total-rainbow connection number*of

*G*, denoted by

*trc*(

*G*), is the minimum number of colors required in a total-coloring...

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 1 > 381-390

*P*in a total-colored graph

*G*is called a total-proper path if (1) any two adjacent edges of

*P*are assigned distinct colors; (2) any two adjacent internal vertices of

*P*are assigned distinct colors; and (3) any internal vertex of

*P*is assigned a distinct color from its incident edges of

*P*. The total-colored...

Graphs and Combinatorics > 2017 > 33 > 4 > 999-1008

*G*is called

*a rainbow tree*if no two edges of it are assigned the same color. For a vertex subset $$S\subseteq V(G)$$ S ⊆ V ( G ) , a tree is called an

*S*-

*tree*if it connects

*S*in

*G*. A

*k*-

*rainbow coloring*of

*G*is an edge-coloring of

*G*having the property that for every set

*S*of

*k*vertices of

*G*, there exists a rainbow

*S*-tree in

*G*. The minimum number...

Journal of Animal Science and Biotechnology > 2017 > 8 > 1 > 1-8

Journal of Solid State Electrochemistry > 2017 > 21 > 4 > 1101-1109

^{−1}at the pore size of 4.1 nm among as-prepared nitrogen-free materials with different sizes. Meanwhile, the nitrogen doping of mesoporous carbon helps...

Journal of Combinatorial Optimization > 2017 > 34 > 2 > 441-452

*G*is a function $$f:V\rightarrow N$$ f : V → N such that $$f(x)\ne f(y)$$ f ( x ) ≠ f ( y ) for every edge $$xy\in E$$ x y ∈ E . A proper coloring of a graph

*G*such that for every $$k\ge 1$$ k ≥ 1 , the union of any

*k*color classes induces a $$(k-1)$$ ( k - 1 ) -degenerate...

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 4 > 1681-1695

*T*in an edge-colored graph is a

*proper tree*if no two adjacent edges of

*T*receive the same color. Let

*G*be a connected graph of order

*n*and

*k*be a fixed integer with $$2\le k\le n$$ 2≤k≤n . For a vertex subset $$S \subseteq V(G)$$ S⊆V(G) with $$\left| S\right| \ge 2$$ S≥2 , a tree containing all the vertices of

*S*in

*G*is called an

*S*-tree. An edge-coloring of

*G*is called a

*k*-

*proper coloring*...

Journal of Combinatorial Optimization > 2017 > 34 > 1 > 165-173

*G*, the smallest number of colors that are needed in order to make

*G*proper connected is called the proper connection number of...

Journal of Combinatorial Optimization > 2017 > 33 > 4 > 1443-1453

*T*in an edge-colored (vertex-colored) graph

*H*is called a

*monochromatic (vertex-monochromatic) tree*if all the edges (internal vertices) of

*T*have the same color. For $$S\subseteq V(H)$$ S ⊆ V ( H ) , a

*monochromatic (vertex-monochromatic) S-tree*in

*H*is a monochromatic (vertex-monochromatic) tree of

*H*containing the vertices of

*S*. For a connected graph

*G*and a given integer

*k*with...

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 3 > 1199-1209

*P*in an edge-colored graph

*G*is called a proper path if no two adjacent edges of

*P*are colored the same, and

*G*is proper connected if every two vertices of

*G*are connected by a proper path in

*G*. The proper connection number of a connected graph

*G*, denoted by $$\textit{pc}(G)$$ pc(G) , is the minimum number of colors that are needed to make

*G*proper connected. In this paper, we investigate the...

*g*(

*D*) of a digraph

*D*and the minimum outdegree

*δ*

^{ + }(

*D*) of

*D*. The special case when

*g*(

*D*) = 3 has lately attracted wide attention. For an undirected graph

*G*, the binding number $bind(G)\geq \frac 3 2$ is a sufficient condition for

*G*to have a triangle (cycle with length 3). In this paper we generalize the concept...

*G*= (

*V*,

*E*) be an edge-colored graph. A matching of

*G*is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is NP-complete. This means that to find both sufficient and necessary good conditions for the existence of perfect heterochromatic...

Bulletin of the Malaysian Mathematical Sciences Society > 2017 > 40 > 1 > 321-333

*G*. Let $$S(G^\sigma )$$ S ( G σ ) be the skew-adjacency matrix of $$G^\sigma $$ G σ . The skew energy of $$G^\sigma $$ G σ is defined as the sum of the absolute values of all eigenvalues of $$S(G^\sigma...

Graphs and Combinatorics > 2016 > 32 > 5 > 1829-1841

*G*, the minimum number of colors that are needed to make

*G*rainbow connected is called the rainbow connection number of

*G*, denoted by rc(

*G*). In this paper,...