Open AccessOn the gracefulness of the graph P 2m,2n
Author(s) -
Zhicheng Liang,
Huijuan Zuo
Publication year - 2010
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm1000003l
Subject(s) - mathematics , combinatorics , graph , discrete mathematics , graph power , disjoint sets , line graph
Let $P_{a,b}$ denotes a graph obtained by identifying the endvertices of $b$ internally disjoint paths each of length $a.$Kathiresan conjectured that graph $P_{a,b}$ is graceful exceptwhen $a$ is odd and $bequiv 2$ (mod 4). In this paper we showthat the graph $P_{a,b}$ is graceful when both $a$ and $b$ areeven