Volume 21 | Number 1 | Year 2015 | Article Id. IJMTT-V21P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V21P507

Alavi et al[1] defined Ascending Subgraph Decomposition(ASD) as decomposition of G with size n + 1 2 into n subgraphs G1,G2,G3, . . . ,Gn without isolated vertices such that each Gi is isomorphic to a proper subgraph of Gi+1 for 1 i n–1 and |E(Gi )| = i for 1 i n. Let G be a graph of size n 2 (2a + (n – 1)d) where a, n, d are positive integers. Then G is said to have (a,d) - Ascending Subgraph Decomposition ((a,d) -ASD) into n parts if the edge set of G can be partitioned into n non-empty sets generating subgraphs G1,G2, . . .,Gn without isolated vertices such that each Gi is isomorphic to a proper subgraph of Gi+1 for 1 i n–1 and |E(Gi)| = a + (i–1)d for 1 i n. The cartesian product G1 x G2 of two graphs G1 and G2 is defined to be the graph whose vertex set is V1 x V2 and two vertices u = (u1,u2) and v = (v1,v2) in V = V1 x V2 are adjacent in G1 x G2 if either u1 = v1 and u2 is adjacent to v2 or u2 = v2 and u1 is adjacent to v1. In this paper, I investigate the (a,d) - Ascending Subgraph Decomposition of Pn+1 x K2.

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S. Asha, "The (A,D) - Ascending Subgraph Decomposition of Cartesian Product of
some Simple Graphs," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 21, no. 1, pp. 52-57, 2015. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V21P507