The(d,1)-total Labelling Of Some Classes Of Graphs

A(d,l)-total labelling of G is an integer-valued function defined on the set V(G)U E(G)such thatA(d,1)-total labelling taking values in the set[0,k]is called a[k]-(d,1)-total labelling of G.The span of a(d,1)-total labelling of G is the maximum difference between any two labels.The(d,1)-total number of G,denoted by λdT(G),is the minimmum span for which G is(d,1)-total labelled.The content of this paper consists of four primary parts:In the first part:As an introduction,we introduced the research background of(d,l)-total labelling and the preliminaries for reading this paper.In the second part:We consider the(d,1)-tota1 labelling of squale of a path Pl2 and the Cartesian product graph Pl2□Km,n,and we obtain the exact values of λdT(Pl2)andλdT(Pl2□Km,n)under the restricted conditions for d.In the third part:We consider the(d,1)-total labelling of square of a cycle Cl2 and the Cartesian product graph Cl2□Km,n,and we obtain the exact values of λdT(Cl2)andλdT(Cl2□Km,n)under the restricted conditions for d.In the final part:The(d,l)-total labelling of Cl3 are studied,and its(d,1)-total number under the restricted conditions for d is obtained.