Up-Embeddability of a Graph by Order and Girth

Let G be a connected graph of order n and girth g. If dG(u) + dG(v) ≥ n − 2g + 5 for any two non-adjacent vertices u and v, then G is up-embeddable. Further more, the lower bound is best possible. Similarly the result of k-edge connected simple graph with girth g is also obtained, k = 2, 3. Key words. Maximum genus, order, Girth, Up-Embeddable.

• Type: Journal
• Year: 2007
• Where: GC
• Authors: Yichao Chen, Yanpei Liu
• Keywords: Applied Computing, Connected Graph, GC 2007, Lower Bound, Non-adjacent Vertices