Connections between labellings of trees

Document Type : Research Paper

Authors

1 College of Mathematics and Statistics‎, ‎Northwest‎ ‎Normal University‎, ‎Lanzhou‎, ‎730070‎, ‎China.

2 School of Mathematics and Statistics‎, ‎Beijing Institute of Techology‎, ‎Beijing 100081‎, ‎China.

3 Department of Information Process and Control Engineering‎, ‎Lanzhou Petrochemical College of Vocational Technology‎, ‎Lanzhou‎, ‎730060‎, ‎China.

Abstract

There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.

Keywords

Main Subjects


B.D‎. ‎Acharya and .M‎. ‎Hegde‎, ‎Arithmetic‎ ‎graphs‎, ‎J‎. ‎Graph Theory 14 (1990)‎, ‎no‎. ‎3‎, ‎275--299‎.
J.A‎. ‎Gallian‎, ‎A dynamic survey of graph labeling‎, ‎Electron‎. ‎J‎. ‎Combin. 16 (2010) 1--246‎.
S.M‎. ‎Hegde‎, ‎On $(k,d)$-graceful graphs‎, ‎J‎. ‎Combin‎. ‎Inform‎. ‎System Sci. 25 (2000)‎, ‎no‎. ‎1-4‎, ‎255--265‎.
B‎. ‎Yao‎, ‎H‎. ‎Cheng‎, ‎M‎. ‎Yao and M‎. ‎Zhao‎, ‎A note on strongly‎ ‎graceful trees‎, ‎Ars Combin. 92 (2009) 155--169‎.
X‎. ‎Zhou‎, ‎B‎. ‎Yao and X‎. ‎Chen‎, ‎Every lobster is odd-elegant‎, ‎Inform‎. ‎Process‎. ‎Lett. 113 (2013)‎, ‎no‎. ‎1-2‎, ‎30--33‎.
X‎. ‎Zhou‎, ‎B‎. ‎Yao‎, ‎X‎. ‎Chen and H‎. ‎Tao‎, ‎A proof to the‎ ‎odd-gracefulness of all lobsters‎, ‎Ars Combin. 103 (2012) 13--18‎.