Name
Abstract | ||
|---|---|---|
A (2,1)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set {0,1,...,k} of nonnegative integers such that |f(x)-f(y)|=2 if x is a vertex and y is an edge incident to x, and |f(x)-f(y)|=1 if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G)@?E(G). The (2,1)-total labeling number @l"2^T(G) of G is defined as the minimum k among all possible (2,1)-total labelings of G. In 2007, Chen and Wang conjectured that all outerplanar graphs G satisfy @l"2^T(G)==5. In this paper, we solve their conjecture, by proving that @l"2^T(G)= |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jda.2011.12.020 | Clinical Orthopaedics and Related Research |
Keywords | DocType | Volume |
total labelings,outerplanar graph,adjacent vertex,adjacent edge,edge set e,minimum k,graph g,edge incident,nonnegative integer,2 1,maximum degree | Journal | 14, |
ISSN | Citations | PageRank |
1570-8667 | 4 | 0.44 |
References | Authors | |
8 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Toru Hasunuma | 1 | 142 | 16.00 |
| Toshimasa Ishii | 2 | 110 | 17.03 |
| Hirotaka Ono | 3 | 400 | 56.98 |
| yushi uno | 4 | 222 | 28.80 |