Cordial Labeling Of K-Shell And Irregular Total Labeling Of Some Graphs

Graph theory is an important branch of discrete mathematics, and discrete mathematics is the ideological foundation of computer science and technology. Graph theory not only applies to a wide range of subjects such as Mathematics, Physics, Geography, Biological and Chemistry, but also to information science, economy and other science. Labeling is an important problem in Graph theory. This paper research cordial labeling and irregular total labeling.A shell graph of order n denoted by H(n,n-3) is the graph obtained from cycle C_n of order n by adding n- 3 chords incident with a common vertex say u. Let v be a vertex adjacent to u in C_n. Sethuramam and Selvaraju conjectured that for all k≥1, and for all n_i≥4,1≤i≤k, one edge union of k-shell graphs H(n_i, n_i - 3) is cordial.To prove one edge union of k-shell graph is cordial, firstly fix the labeling of vertex of common edge(label u with 0 and v with 1), then according to the value of the graph order n module 4 to class the k shell gaphs to four cases, and to divide to small cases in every shell graph. At last, we prove the labeling is right according to the definition of cordial labeling. So we resolve the Sethuramam and Selvaraju conjecture successfully.Ba(?)a defined the irregular total labeling and the strength irregular total labeling. We denote strength vertex irregular total labeling and strength edge irregular total labeling by tvs(G) and tes(G) respectively. This paper proved:...