Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Mathew, Jess

doi:10.18831/djmaths.org/2015011005

Cited by 4 publications

(5 citation statements)

References 4 publications

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“…A monophonic path is a path if it contains no chord. The length of the longest x-y monophonic path of a graph G is called the monophonic distance dm(x,y) for every vertices x,y in G. A monophonic path from x to y with length dm(x,y) is called an x -y monophonic "as stated in [1,2,3,4]". Consider a graph H, since other graphs or networks are embedded into it , as host graph and graphs or networks which are embedded in H are called guest graph "as given in [5,6,7]".…”

Section: Introductionmentioning

confidence: 99%

Monophonic wirelength on Circulant Networks

Samundesvari¹,

Michael²

2018

IJET

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In this paper, we define the monophonic embedding of graph G into graph H and we present an algorithm for finding the monophonic wirelength of circulant networks into the family of grids M(n×2), n≥2.The monophonic embedding of a graph G into a graph H is an embedding denoted by fm is a bijective map from the vertex set of G into the vertex set of H and fm is a one-one mapping from the edge set (x, y) of G into Pm(H) where Pm(H) is the set of monophonic paths between fm(x) and fm(y) for every fm(x), fm(y) H. The monophonic wirelength of fm of G into H is the sum of distances of monophonic paths between two vertices fm(x) and fm(y) in H such that (x, y) E(G). This paper presents a monophonic algorithm to find the monophonic wirelength of circulant networks G(2n, ±S) , where S  {1,2,3,…,n} into the family of grids M[n×2],n≥2. We also derived a Lemma to get the monophonic edge congestion MEC (G,H).

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Section: Introductionmentioning

confidence: 99%

Monophonic wirelength on Circulant Networks

Samundesvari¹,

Michael²

2018

IJET

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“…By an embedding f : G → H and a monophonic embedding fm: GH, it is meant that the graphs G(V, E) and H(V, E) are finite, simple and connectedwith n vertices. Given a host graph H, which represents the network into which other networks are to be embedded, and a guest graph G, which represents the network to be embedded, the problem is to find a mapping from V(G) to V(H) such that each edge of G can be mapped to a path in Has given in [3][4][5][6][7]. An embedding f of G into H is defined as follows:…”

Section: Introductionmentioning

confidence: 99%

Monophonic Wirelength in Graph Embedding

Michael¹,

Samundesvari²

2018

IJET

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In this paper we consider the monophonic embedding ofcirculant networks into cycles and we produce an algorithmto get the monophonic wirelength of the same.Further wend that the monophonic wirelength of some family of cir-In this paper, we define the monophonic embedding of graph G into another graph H and this paper presents a monophonic algorithm to find the monophonic wirelength of circulant networks G[n, ±S], where S ⊆ {1,2,3,…,n/2} into the family of Cycle Cn, n≥ 4. The mono-phonic embedding of a graph G into a graph H is an embedding denoted by fmis a bijective map from the vertex set of G into the vertex set of H and fm is a one-one mapping from the edge set (x, y) of G into Pm(H) where Pm(H) is the set of monophonic paths between fm(x) and fm(y) for every fm(x), fm(y) ∈ H. The monophonic wirelength of fm of G into H is the sum of distances of monophonic paths between two vertices fm(x) and fm(y) in H such that (x, y) ∈ E(G). In addition, the eccentricity, radius and diameter of an embedding of G into H are defined. The average wirelength of an embedding is defined and the bounds of average wirelength of some embeddings have been found.

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“…The method of VIM, that was suggested initially by [1][2][3][4], was evinced by several authors to exist as a potent tool for mathematics when it comes for problems like linear and nonlinear ones [5][6][7][8][9][10][11][12][13][14][15]. In contrast to the old-style numerical methods, the features of discretization, linearization, transformation or perturbation is no longer in need for VIM.…”

Section: Introductionmentioning

confidence: 99%

Variational Iteration Method for Burger’s Equation in Different Positions

Anjum¹,

Suleman²,

Rahman³

2017

IJMNP

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The method of variational iteration was found to pave an exact way to solve the Burger's equation at various locations. The Variational Iteration Method (VIM) was proved to be efficacious, potent, straightforward and not complicated, when matched with various techniques. This made this method to exhibit its implementation in all aspects of problems which fall under physics as well as problems related to mathematics, linear and nonlinear ones.

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Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Cited by 4 publications

References 4 publications

Monophonic wirelength on Circulant Networks

Monophonic wirelength on Circulant Networks

Monophonic Wirelength in Graph Embedding

Variational Iteration Method for Burger’s Equation in Different Positions

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