Edge even graceful labeling of some graphs

Abstract

Abstract Edge even graceful labeling is a new type of labeling since it was introduced in 2017 by Elsonbaty and Daoud (Ars Combinatoria 130:79–96, 2017). In this paper, we obtained an edge even graceful labeling for some path-related graphs like Y- tree, the double star B n,m , the graph 〈K 1,2n :K 1,2m 〉, the graph P2n−1⊙K2m¯ $ ~P_{2n-1}\odot \overline { K_{2m}}~ $, and double fan graph F 2,n . Also, we showed that some cycle-related graphs like the prism graph ∏n $ ~\prod _{n}~ $, the graph Cnn2 $ ~C_{n}\left (\frac {n}{2}\right)~ $, the flag FL n , the graph K 2⊙C n , the flower graph FL(n), and the double cycle {C n,n } are edge even graphs.

Keywords

• Edge-even graceful labeling
• Flag graph FL n
• Double fan graph F 2,n
• Prism graph
• The flower graph FL(n)