Name
Abstract | ||
|---|---|---|
For a graph G of order vertical bar V(G)vertical bar = n and a real-valued mapping f : V(G) -> R, if S subset of V(G) then f (S) = Sigma(w is an element of S) f (w) is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, NS[f] = max{f (N[v])vertical bar v is an element of V(G)} and NS(f) = max{f (N(v))vertical bar v is an element of V(G)}. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, NS-[f] = min{f (N[v])vertical bar v is an element of V(G)} and NS-(f) = min{f (N(v))vertical bar v is an element of V(G)}. For W subset of R, the closed and open neighborhood sum parameters are NSW[G] = min{NS[f]vertical bar f : V(G) -> W is a bijection} and NSW(G) = min{NS(f)vertical bar f : V(G) -> W is a bijection}. The lower neighbor sum parameters are NSW-[G] = max{NS-[f]vertical bar f : V(G) -> W is a bijection} and NSW-(G) = max{NS-(f)vertical bar f : V(G) -> W is a bijection}. For bijections f : V(G) -> {1, 2,..., n} we consider the parameters NS[G], NS(G), NS-[G] and NS-(G), as well as two parameters minimizing the maximum difference in neighborhood sums. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s11786-011-0075-4 | Mathematics in Computer Science |
Keywords | Field | DocType |
Graph labeling, Sigma labeling, Neighborhood sums | Graph,Discrete mathematics,Combinatorics,Bijection,Graph labeling,Bijection, injection and surjection,Mathematics | Journal |
Volume | Issue | ISSN |
5 | 1 | 1661-8270 |
Citations | PageRank | References |
1 | 0.60 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Allen O'Neal | 1 | 4 | 1.86 |
| Peter J. Slater | 2 | 593 | 132.02 |