Some New Graph Labeling Problems : A
نویسنده
چکیده
All \labelings" discussed in this paper are vertex labelings. We call a labeling l of G an N -labeling if there exists a connected induced subgraph H of G with Px2V (H) l(x) = i for every integer i, 1 i N . Then c(G) is the largest integer N such that G has an N labeling. A labeling l of G is called irredundant if, for all connected induced subgraphs H1 and H2, Px2V (H1) l(x) = Px2V (H2) l(x) if and only if H1 = H2. Then p(G) is the smallest integer N such that there exists an irredundant labeling l of G with Px2V (G) l(x) = N . In this report, we study c(G) and p(G) in the cases where G is a complete graph minus one edge, a star, a path, or a cycle. We obtain some preliminary results, but there are many interesting questions left open.
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