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Reseach Article
Edge Rotations, Edge Jumps and its Effect on Certain Graph Parameters
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 186 - Number 25 |
| Year of Publication: 2024 |
| Authors: Chitra Ramaprakash |
10.5120/ijca2024923729
|
Chitra Ramaprakash . Edge Rotations, Edge Jumps and its Effect on Certain Graph Parameters. International Journal of Computer Applications. 186, 25 ( Jul 2024), 41-44. DOI=10.5120/ijca2024923729
Abstract
Let S be a set of graphs on which a measure of distance (a metric) has been defined. The distance graph D(S) of S is that graph with vertex set S, such that two vertices(graphs) G and H are adjan- cent if and only if the distance between G and H is one. A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v and w such that uv ∈ E(G), uw ∈/ E(G) and H ∼=G − uv + uw. In this case, G is transformed into H by “rotating” the edge uv of G into uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u, v, w and x such that uv∈ E(G), wx ∈/ E(G) and H ∼= G − uv + wx. In this paper, I investigate the effect of the above mentioned edge operations viz., rotation and jump on certain graph parameters. I investigate rotations on DDR graphs, rotations on cycles, paths, Eulerian graphs, eccentric digraphs and the planarity property of the connected graph post edge rotation. We also present an algorithm that generates all rotation distance graphs at distance one.
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