The Journal of the Indian Mathematical Society

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Graph Equations Involving Line Graphs, Middle Graphs and Mediate Graphs


Affiliations
1 Department of Mathematics, Pondicherry University, Puducherry - 605 014, India
2 Department of Mathematics, Karnatak University, Dharwad - 580 003, India
     

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In this paper, we obtain all pairs (G,H) of graphs satisfying the following graph equations:

Keywords

Line Graph, Middle Graph, Mediate Graph, Eulerian, Outer- Planar, Maximal Outerplanar, Minimally Nonouterplanar.
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  • L.W. Beineke, Derived graphs and digraphs, Beitrge Zur Graphentheorie, Leipzig, (1968), 17–23.

  • T. Hamada and I. Yoshimura, Traversability and connectivity of the middle graph of a graph, Discrete Math., 14 (1976), 247–255.

  • F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, 1969.

  • H. P. Patil, B. Basavanagoud and V. Ramakrishna, Connectivity, traversability, planarity and coverings in mediate graphs, J. Karnatak Univ. Sci., 2013, 38–48.

  • H. Whitney, Congruent graphs and the connectivity of graphs, Amer. J. Math. 54 (1932), 150–168.


Abstract Views: 236

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  • Graph Equations Involving Line Graphs, Middle Graphs and Mediate Graphs

Abstract Views: 236  |  PDF Views: 0

Authors

H. P. Patil
Department of Mathematics, Pondicherry University, Puducherry - 605 014, India
B. Basavanagoud
Department of Mathematics, Karnatak University, Dharwad - 580 003, India
V. Ramakrishnan
Department of Mathematics, Pondicherry University, Puducherry - 605 014, India

Abstract


In this paper, we obtain all pairs (G,H) of graphs satisfying the following graph equations:

Keywords


Line Graph, Middle Graph, Mediate Graph, Eulerian, Outer- Planar, Maximal Outerplanar, Minimally Nonouterplanar.

References