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On super vertex-graceful unicyclic graphs
Authors:Sin-Min Lee  Elo Leung  Ho Kuen Ng
Affiliation:(1) Department of Computer Science, San Jose State University, San Jose, California, 95192, U.S.A.;(2) Department of Mathematics, San Jose State University, San Jose, California, 95192, U.S.A.
Abstract:A graph G with p vertices and q edges, vertex set V(G) and edge set E(G), is said to be super vertex-graceful (in short SVG), if there exists a function pair (f, f +) where f is a bijection from V(G) onto P, f + is a bijection from E(G) onto Q, f +((u, v)) = f(u) + f(v) for any (u, v) ∈ E(G),
$$
Q = left{ begin{gathered}
  {  pm 1, ldots , pm tfrac{1}
{2}q} ,                 if q is even, hfill 
  { 0, pm 1, ldots , pm tfrac{1}
{2}(q - 1)} ,     if q is odd, hfill  
end{gathered}  right.
$$
and
$$
P = left{ begin{gathered}
  {  pm 1, ldots , pm tfrac{1}
{2}p} ,                 if p is even, hfill 
  { 0, pm 1, ldots , pm tfrac{1}
{2}(p - 1)} ,     if p is odd. hfill  
end{gathered}  right.
$$
We determine here families of unicyclic graphs that are super vertex-graceful.
Keywords:graceful  edge-graceful  super edge-graceful  super vertex-graceful  amalga-mation  trees  unicyclic graphs
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