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4 papers · 2 filters
Nordhaus-Gaddum-type theorem for total proper connection number of graphs
Wenjing Li, Xueliang Li, Jingshu Zhang
A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A path in a total-colored graph is called a \emph{total-proper path}…
3-Rainbow index and forbidden subgraphs
Wenjing Li, Xueliang Li, Jingshu Zhang
A tree in an edge-colored connected graph is called \emph{a rainbow tree} if no two edges of it are assigned the same color. For a vertex subset , a tree is ca…
On two conjectures about the proper connection number of graphs
Fei Huang, Xueliang Li, Zhongmei Qin +2
A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph , the proper connection number of…
Path connectivity of line graphs
Yaping Mao
Dirac showed that in a -connected graph there is a path through each vertices. The path -connectivity of a graph , which is a generalization of Dirac's no…