| Full text | |
| Author(s): |
Luiz, Atilio G.
;
Campos, C. N.
;
Richter, R. Bruce
Total Authors: 3
|
| Document type: | Journal article |
| Source: | GRAPHS AND COMBINATORICS; v. 36, n. 6, p. 19-pg., 2020-09-03. |
| Abstract | |
An injection f:V(T)->{0,...,vertical bar E(T)vertical bar} of a tree T is a graceful labelling if {vertical bar f(u)-f(v)vertical bar:uv is an element of E(T)}={1,..., vertical bar E(T)vertical bar}. Tree T is 0-rotatable if, for any v is an element of V(T), there exists a graceful labelling f of T such that f(v)=0. In this work, the following families of caterpillars are proved to be 0-rotatable: caterpillars with a perfect matching; caterpillars obtained by linking one leaf of the star K-1,K-s-1 to a leaf of a path P-n with n >= 3 and s >= left [n/2]; caterpillars with diameter five or six; and caterpillars T with diam (T)>= 7 such that, for every non-leaf vertex v is an element of V(T), the number of leaves adjacent tovis even and is at least 2+2((diam(T)-1)mod2). These results reinforce the conjecture that all caterpillars with diameter at least five are 0-rotatable. (AU) | |
| FAPESP's process: | 14/16861-8 - Problems on graph labelling |
| Grantee: | Atilio Gomes Luiz |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 14/16987-1 - Selected structural problems in graph theory |
| Grantee: | Christiane Neme Campos |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 15/03372-1 - Some labelling problems on graphs |
| Grantee: | Atilio Gomes Luiz |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |