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Award ID contains: 1659075

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  1. ; ; ; (, Electronic Journal of Graph Theory and Applications)
    null (Ed.)
    Full Text Available 
  2. ; ; ; ; ; (, AKCE International Journal of Graphs and Combinatorics)
    null (Ed.)
    Full Text Available 
  3. (, Involve)
    A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. We present a complete classification of all connected edge-transitive graphs on less than or equal to 20 vertices. We investigate biregular bipartite edge-transitive graphs and present connections to combinatorial designs, and we show that the Cartesian products of complements of complete graphs give an additional family of edge-transitive graphs. 
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    Accepted Manuscript Full Text Available
  4. (, AKCE International Journal of Graphs and Combinatorics)
    A k-ranking of a graph G is a labeling with k labels such that if f(u) = f(v) then every uv path contains a vertex w such that f(w) > f(u). The rank number of G, denoted Xr (G), is the minimum k such that a k-ranking exists for G. In this paper we characterize graphs with large rank numbers. In addition, we characterize subdivided stars based on their rank numbers. 
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    Accepted Manuscript Full Text Available