$C_4$ and $C_6$ decomposition of the tensor product of complete graphs

Oyewumi, Opeyemi; Akwu, Abolape Deborah

doi:10.48550/arxiv.1908.00172

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“…Chao -Chih Chou et al [3] obtained the decomposition of complete bipartite graph K m,n into p copies of C 4 , q copies of C 6 and r copies of C 8 , if m ≥ 4, n ≥ 6 and m, n are even, and the same kind of decomposition exists in K m,n − I where I is a 1-factor of K m,n , if n is odd. Many authors discussed the multi -decomposition as combination of stars with cycles or paths in complete multi -graphs, complete bipartite graphs and product graphs [1,4,5,6,7,8,10,11,12,13,14,15,16,18]. All these studies motivate us to study the multi -decomposition of K m,n into stars and bowties of size l for the given positive integers m, n and l.…”

Section: P Hemalatha and K Ramyamentioning

confidence: 99%

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Multi - Decomposition of Complete Bipartite Graphs into Stars and Bowties of Size l

Hemalatha,

Ramya

2023

GJPAM

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Let K m,n denotes a complete bipartite graph with vertex partitions of cardinality m and n. A star S l denotes a complete bipartite graph K 1,l . A Bowtie B l is a graph formed by the union of two cycles of length l/2 intersecting at a common vertex whenever l is even. A decomposition of a graph G is a collection of edge disjoint subgraphs H such that every edge of G belongs to exactly one H. Given non -isomorphic subgraphs H 1 and H 2 of G, a (H 1 , H 2 ) multi -decomposition of G is the decomposition of G into a copies of H 1 and b copies of H 2 , such that aH 1 ⊕ bH 2 = G, for some integers a, b ≥ 0. In this paper, the multidecomposition of K m,n into S l and B l has been investigated. It is proved that for given positive integers m, n and l, when m ≡ 0(mod l), n ≥ l/2 for l ≡ 0(mod 8) or l ≡ 4(mod 8), K m,n can be decomposed into a copies of S l and b copies of B l for some of the admissible pairs (a, b) if and only if l(a + b) = mn.

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Section: P Hemalatha and K Ramyamentioning

confidence: 99%

“…In this case, if we remove the 8 edges of one S 8 in K 8,12 then the resultant graph K 8,12 \S 8 has odd degree and using that we cannot form 11 bowties. Hence (1,11) is not a suitable pair for the required decomposition in K 8,12 . Case (iii) a = 2, b = 10.…”

Section: Sufficient Conditionsmentioning

confidence: 99%

Multi - Decomposition of Complete Bipartite Graphs into Stars and Bowties of Size l

Hemalatha,

Ramya

2023

GJPAM

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$C_4$ and $C_6$ decomposition of the tensor product of complete graphs

Cited by 1 publication

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Multi - Decomposition of Complete Bipartite Graphs into Stars and Bowties of Size l

Multi - Decomposition of Complete Bipartite Graphs into Stars and Bowties of Size l

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