Enumeration of Glued Graphs of Paths

Authors

  • Monthiya Ruangnai PhD Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200
  • Sayan Panma Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200

DOI:

https://doi.org/10.26713/cma.v10i4.1252

Keywords:

A glued graph, The glue operator, Glued graph of paths, Graphs enumeration, Graph isomorphisms

Abstract

Let \(G_1\) and \(G_2\) be two vertex-disjoint graphs with \(H_1\) a subgraph of \(G_1\) and \(H_2\) a subgraph of \(G_2\). Let \(f:H_1 \rightarrow H_2\) be an isomorphism between these subgraphs. The glued graph of \(G_1\) and \(G_2\) at \(H_1\) and \(H_2\) with respect to \(f\) is the graph that results from combining \(G_1 \cup G_2\) by identifying the subgraphs \(H_1\) and \(H_2\) according to the isomorphism \(f\) between \(H_1\) and \(H_2\). We refer \(G_1\) and \(G_2\) as its original graphs and refer \(H\) as its clone where \(H\) is a copy of \(H_1\) and \(H_2\). In this paper, we enumerate all non-isomorphic resulting glued graphs between two paths at connected clones. Moreover, we also give the characterization of the glued graph at a connected clone.

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References

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Published

31-12-2019
CITATION

How to Cite

Ruangnai, M., & Panma, S. (2019). Enumeration of Glued Graphs of Paths. Communications in Mathematics and Applications, 10(4), 783–796. https://doi.org/10.26713/cma.v10i4.1252

Issue

Vol. 10 No. 4 (2019)

Section

Research Article

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