| G-Ringel made the conjecture in 1963 that many fields in modern life are based on the theory of graph theory as the basic framework.In particular,the problem of labeled graph is extremely extensive and it makes a great contribution to social life.There are many kinds of labeled graph researches.The study of graceful graph has always been very popular.The main research of this paper is the odd graceful labeling which derives from graceful graph.Gnanajothi defined a graph G with q edges to be odd graceful if there is an injection f from V(G)to {0,1,2,...,2q-1} such that,when each edge xy is assigned the label |f(x)-f(y)|,the resulting edge are {1,3,5...,2q-1}.She proved that the class of odd graceful graphs lies between the class of graphs with a-labelings and the class of bipartite graphs by showing that every graph with an a-labeling has an odd graceful labeling and every graph with an odd cycle is not odd graceful.So far,a great deal of achievements have been made in the research on serpentine graph both at home and abroad.This paper defines a new serpentine graph,namely the nCm1,m2,…,mn-snake,and studies its odd gracefulness.The paper separately discusses when mi = O(mod 4),mi≡2(mod 8),mi≡6(mod 8),mi≠6(where i is even)nCm1,m2,…,mn-snakes is odd graceful graph.The paper made a corresponding proof and finally reached a conclusion. |
