Country：United States

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Language：English

Event date： 2015.1

Language：English   Presentation type：Oral presentation (general)  

Country：United States  

Event date： 2014.10

Language：English   Presentation type：Oral presentation (invited, special)  

Country：United States  

Event date： 2013.3

Language：English   Presentation type：Oral presentation (general)  

Country：United States  

Every connected graph G contains a closed walk in which every vertex in G appears at least once. Such a walk is a (vertex) covering walk in G. In particular, a shortest such walk is called a Hamiltonian walk in G and its length is called the Hamiltonian number of G. These concepts were introduced by S. E. Goodman and S. T. Hedetniemi in 1973 and have been studied by many. Some recent results and related topics in this area will be discussed.

Event date： 2012.11

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

There have been numerous studies using a variety of methods for the purpose of uniquely identifying the vertices of a graph or distinguishing two vertices whenever they are adjacent. Naturally, many of these methods involve graph colorings and labelings. A graph coloring that allows us to distinguish every two adjacent vertices in a given graph in some manner is said to be neighbor-distinguishing. On the other hand, a graph coloring is vertex-distinguishing if the coloring provides us with a way to distinguish every two vertices in a graph regardless of whether they are adjacent or not.
In this talk, some edge labelings that give rise to ways of distinguishing vertices are introduced. Let G be a connected graph of size at least 2 and c an edge labeling of G using k labels, say 1, 2, ... , k, where adjacent edges may be assigned the same label. For each vertex v of G, the code of v with respect to c is the k-vector whose i-th coordinate is the number of edges incident with v that are labeled i. The labeling c is called a detectable labeling of G if distinct vertices in G have distinct codes, that is, a detectable labeling of a graph is a vertex-distinguishing edge labeling of the graph. We discuss some recent results in this area of research and related topics.

Event date： 2012.10

Language：English   Presentation type：Oral presentation (general)  

Country：United States  

Every connected graph G contains a closed walk in which every vertex in G appears at least once. Such a walk is a (vertex) covering walk in G. In particular, a shortest such walk is called a Hamiltonian walk in G and its length is called the Hamiltonian number of G. These concepts were introduced by S. E. Goodman and S. T. Hedetniemi in 1973 and have been studied by many. In this talk, we discuss some recent results in this area and related topics.

Audience： Junior students,　High school students,　Teachers

Type：Visiting lecture

Audience： Junior students,　High school students,　Teachers

Type：Visiting lecture

Audience： Junior students,　High school students,　Teachers

Type：Visiting lecture