Antipodal Embeddings of Graphs

Farzan, M.; Waller, Derek A.

doi:10.1112/jlms/s2-15.3.377

Cited by 10 publications

(2 citation statements)

References 5 publications

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“…An antipodal graph G with diameter D has the property that each node veG has an unique (antipodal) node U of distance D from v in G. The antipodal node-pairs in G produce a quotient graph H with a double cover projection p : G ---+ H (Sub-Section 2.1). Any antipodal graph G has circuits of length 2D passing through antipodal node-pairs [15]. Here the 'block system' of a graph comes in, which allows to derive a quotient graph whose nodes correspond with the blocks (Note the intersection of the embedded mN-gon prism switches in Sub-Section 3.2 are antipodal graphs).…”

Section: Antipodal Graphmentioning

confidence: 99%

New directions in modelling, analysis and design of WDM/OFDM-networks: (I) Optical Switching

Giglmayr

1998

Optical Network Design and Modelling

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Bearing in mind that a topological representation of a finite graph is a compact space, by the relationships between (Graph)Topology, Algebraic Topology, Group Theory, (Differential)Geometry and Combinatorics a new universe arises for modelling, analysis and design of (telecommunication) networks_ Throughout the present paper, coverings/covering spaces, the lifting problem and quotient graphs are briefly interpreted in terms of the requirements for the combinatorial design of optical switches though the presentation is mainly based on illustrations rather than on a (precise) mathematical description.

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Section: Antipodal Graphmentioning

confidence: 99%

New directions in modelling, analysis and design of WDM/OFDM-networks: (I) Optical Switching

Giglmayr

1998

Optical Network Design and Modelling

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show abstract

“…Concurrently, he wrote papers [3,9,10,11,14] concerned with the properties of the adjacency matrix of a graph: the paper [11] is a particularly attractive synthesis of geometric and algebraic methods, applied to clique numbers and interchange graphs. The interplay between abstract ideas and their geometrical realisation was also the motivation for his work on the imbedding of graphs in surfaces [13,20],…”

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confidence: 99%