(a,d)-Continuousmonotonic Subgraph Decomposition of K_(n+1) and Integral Sum Graphsg_(0,n)

10.5556/j.tkjm.46.2015.1432

K. Vilfred；A. Suryakala

Tamkang Journal of Mathematics

46卷1期（2015 / 03 / 01）

31 - 49

英文

For a,d,n ∈N,we define (a,d)-Cont inuous Monotonic SubgraphDecomposition or (a,d)-CMSD of a graphG of size □ as the decomposition ofG into n subgraphs G1,G2, . . . ,Gn without isolated vertices such that each Gi is connected and isomorphic to a proper subgraph ofGi+1 and |E(Gi )|=a+(i -1)d for i=1, 2, . . . ,n. (1,1)-CMSD of a graph G is called a Continuous Monotonic Subgraph Decomposition or CMSD of G. Harary introduced the concepts of sum and integral sum graphs and a family of integral sum graphs G-n,n over [-n,n] and it was generalized to G-m,n where [r, s] = {r, r +1, . . . , s}, r, s ∈ Z andm,n ∈N0. In this paper, we study (a,d)-CMSD of Kn+1 andG0,n into families of triangular books, triangular books with book mark and Fans with handle.