TY - JOUR
AU - Ricardo, Luisa
AU - Dantas, Simone
AU - Luiz, Atilio
PY - 2020/11/15
Y2 - 2024/10/14
TI - On the Graceful Game
JF - Revista Eletrônica de Iniciação Científica em Computação
JA - REIC
VL - 18
IS - 3
SE - Edição Especial: CTIC/CSBC
DO - 10.5753/reic.2020.1745
UR - https://journals-sol.sbc.org.br/index.php/reic/article/view/1745
SP -
AB - <p>A graceful labeling of a graph G with m edges consists in labeling the vertices of G with distinct integers from 0 to m such that, when each edge is assigned the absolute difference of the labels of its endpoints, all induced edge labels are distinct. Rosa established two well known conjectures: all trees are graceful (1966) and all triangular cacti are graceful (1988). In order to contribute to both conjectures we study these problems in the context of graph games. The graceful game was introduced by Tuza in 2017 as a two-players game on a connected graph in which the players Alice and Bob take turns labeling the vertices with distinct integers from 0 to m. Alice’s goal is to gracefully label the graph as Bob’s goal is to prevent it from happening. In this work, we present the first results in this area by showing winning strategies for Alice and Bob in complete graphs, paths, cycles, complete bipartite graphs, caterpillars, prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths.</p>
ER -