Folding wheels and fans

If two non-adjacent vertices of a connected graph that have a common neighbor are identified and the resulting multiple edges are reduced to simple edges, then we obtain another graph of order one less than that of the original graph. This process can be repeated until the resulting graph is complet...

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Main Authors: Gervacio, Severino V., Guerrero, Romulo C., Rara, Helen M.
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Published: Animo Repository 2002
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Online Access:https://animorepository.dlsu.edu.ph/faculty_research/3621
https://animorepository.dlsu.edu.ph/context/faculty_research/article/4623/type/native/viewcontent/s003730200058.html
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-46232021-09-20T02:37:09Z Folding wheels and fans Gervacio, Severino V. Guerrero, Romulo C. Rara, Helen M. If two non-adjacent vertices of a connected graph that have a common neighbor are identified and the resulting multiple edges are reduced to simple edges, then we obtain another graph of order one less than that of the original graph. This process can be repeated until the resulting graph is complete. We say that we have folded the graph onto complete graph. This process of folding a connected graph G onto a complete graph induces in a very natural way a partition of the vertex-set of C. We denote by F(G) the set of all complete graphs onto which C can be folded. We show here that if p and q are the largest and smallest orders, respectively, of the complete graph in F(Wn) or F(Fn), then Ks, is in F(Wn) or F(Fn) for each s, q ≤ s ≤ p. Lastly, we shall also determine the exact values of p and q. 2002-12-01T08:00:00Z text text/html https://animorepository.dlsu.edu.ph/faculty_research/3621 info:doi/10.1007/s003730200058 https://animorepository.dlsu.edu.ph/context/faculty_research/article/4623/type/native/viewcontent/s003730200058.html Faculty Research Work Animo Repository Tiling (Mathematics) Quadrilaterals Triangle Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
topic Tiling (Mathematics)
Quadrilaterals
Triangle
Mathematics
spellingShingle Tiling (Mathematics)
Quadrilaterals
Triangle
Mathematics
Gervacio, Severino V.
Guerrero, Romulo C.
Rara, Helen M.
Folding wheels and fans
description If two non-adjacent vertices of a connected graph that have a common neighbor are identified and the resulting multiple edges are reduced to simple edges, then we obtain another graph of order one less than that of the original graph. This process can be repeated until the resulting graph is complete. We say that we have folded the graph onto complete graph. This process of folding a connected graph G onto a complete graph induces in a very natural way a partition of the vertex-set of C. We denote by F(G) the set of all complete graphs onto which C can be folded. We show here that if p and q are the largest and smallest orders, respectively, of the complete graph in F(Wn) or F(Fn), then Ks, is in F(Wn) or F(Fn) for each s, q ≤ s ≤ p. Lastly, we shall also determine the exact values of p and q.
format text
author Gervacio, Severino V.
Guerrero, Romulo C.
Rara, Helen M.
author_facet Gervacio, Severino V.
Guerrero, Romulo C.
Rara, Helen M.
author_sort Gervacio, Severino V.
title Folding wheels and fans
title_short Folding wheels and fans
title_full Folding wheels and fans
title_fullStr Folding wheels and fans
title_full_unstemmed Folding wheels and fans
title_sort folding wheels and fans
publisher Animo Repository
publishDate 2002
url https://animorepository.dlsu.edu.ph/faculty_research/3621
https://animorepository.dlsu.edu.ph/context/faculty_research/article/4623/type/native/viewcontent/s003730200058.html
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