Double Power of 2 Decomposition [DPo2D]
of Graphs

S. Asha; V.G. Smilin Shali

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P515

Double Power of 2 Decomposition [DPo2D] of Graphs

S. Asha, V.G. Smilin Shali

Citation :

S. Asha, V.G. Smilin Shali, "Double Power of 2 Decomposition [DPo2D] of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 122-131, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P515

Abstract

Let G be a finite, connected simple graph with p vertices and q edges. If G1, G2,...., Gn are connected edge-disjoint subgraphs of G with E(G) = E(G1) υ E(G2) υ ... υ E(Gn), then { G1, G2,...., Gn} is said to be a decomposition of G. In this paper we introduce a new concept called Double power of 2 Decomposition of graphs. A graph G is said to have Double Power of 2 Decomposition if G can be decomposed into subgraphs { 2G1, 2G2,...,2Gn} such that each G2, is connected and |E(Gi) = 2i, for 1≤i≤n. Clearly, q = 4[2n-1]. In this paper, we investigate the necessary and sufficient condition for graphs such as J(m,3), Lm, Tm and Hm to accept Double Power of 2 Decomposition.

Keywords

Decomposition of Graph, Power of 2 Decomposition, Double Power of 2 Decomposition.

References

[1] S. Asha and V . G. Smilin Shali , Power of 2 Decomposition of Some Trees and a Spider Tree , Journal of Information and Computational Science , ISSN : 1548 – 7741 , Volume 10 , Issue 3, 2020.
[2] Frank Harary, (1972), Graph Theory, Addison-Wesley Publishing Company.
[3] V.G. Smilin Shali and S. Asha , (2019), Double Arithmetic Odd Decomposition [DAOD] of Some Complete 4-Partite Graphs, International Journal of Innovative Technology and Exploring Engineering, Vol. 9, Issue - 2, December 2019, 3902-3907.
[4] V. G. Smilin Shali and S. Asha , Power of 2 Decomposition of a Complete Tripartite Graph K2,4,m and a Special Butterfly Graph , International Journal of Engineering and Advanced Technology (IJEAT) , ISSN : 2249 – 8958 , Volume 9 , Issue 3 , February, 2020 .
[5] V. G. Smilin Shali and S. Asha , Double Arithmetic Odd Decomposition [DAOD] of Graphs, Journal of Xidian University , ISSN : 1001 – 2400 , Volume 14 , Issue 3, 2020.