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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On 0-Rotatable Graceful Caterpillars

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Author(s):
Luiz, Atilio G. [1] ; Campos, C. N. [2] ; Richter, R. Bruce [3]
Total Authors: 3
Affiliation:
[1] Univ Fed Ceara, Campus Quixada, Fortaleza, Ceara - Brazil
[2] Univ Estadual Campinas, Inst Comp, Sao Paulo - Brazil
[3] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON - Canada
Total Affiliations: 3
Document type: Journal article
Source: GRAPHS AND COMBINATORICS; SEP 2020.
Web of Science Citations: 0
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: 14/16987-1 - 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
FAPESP's process: 14/16861-8 - Problems on graph labelling
Grantee:Atilio Gomes Luiz
Support Opportunities: Scholarships in Brazil - Doctorate