Arithmetic Odd Star Decomposition of Graphs

Merly, E. Ebin Raja (2021) Arithmetic Odd Star Decomposition of Graphs. In: Current Topics on Mathematics and Computer Science Vol. 7. B P International, pp. 17-23. ISBN 978-93-91595-32-6

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Abstract

Let G = (V, E) be a simple connected graph with p vertices and q edges. If G1, G2, …., Gn are connected edge disjoint subgraphs of G with E(G) = E(G1) E(G2) …. E(Gn), then (G1, G2, ……, Gn) is said to be a decomposition of G. A decomposition (G1, G2, ……, Gn) of G is said to be continuous monotonic decomposition if each Gi is connected and |E(Gi)| = i for every i = 1, 2, …., n. [1]. In this chapter, we introduced the concept Arithmetic odd star decomposition. A decomposition (G1, G2, ……, Gn) of G is said be an Arithmetic decomposition if |E(Gi) = a + (i-1)d, for every I = 1, 2 ……, n and a, d Z. Clearly q= [2a + (n - 1) d]. If a = 1 and d = 1, then q = . In this chapter, we study the graphs with a = 1 and d = 2. Then q = n2. That is, the number of edges of G is a perfect square.

Item Type: Book Section
Subjects: Open Research Librarians > Mathematical Science
Depositing User: Unnamed user with email support@open.researchlibrarians.com
Date Deposited: 25 Oct 2023 05:18
Last Modified: 25 Oct 2023 05:18
URI: http://stm.e4journal.com/id/eprint/1799

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