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Class of Crosscap Two Graphs Arising from Lattices–I

Author

Listed:
  • T. Asir

    (Department of Mathematics, Pondicherry University, Pondicherry 605 014, Tamil Nadu, India)

  • K. Mano

    (Department of Mathematics, Fatima College, Madurai 625 018, Tamil Nadu, India)

  • Jehan A. Al-Bar

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21461, Saudi Arabia)

  • Wafaa M. Fakieh

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21461, Saudi Arabia)

Abstract

Let L be a lattice. The annihilating-ideal graph of L is a simple graph whose vertex set is the set of all nontrivial ideals of L and whose two distinct vertices I and J are adjacent if and only if I ∧ J = 0 . In this paper, crosscap two annihilating-ideal graphs of lattices with at most four atoms are characterized. These characterizations provide the classes of multipartite graphs, which are embedded in the Klein bottle.

Suggested Citation

  • T. Asir & K. Mano & Jehan A. Al-Bar & Wafaa M. Fakieh, 2023. "Class of Crosscap Two Graphs Arising from Lattices–I," Mathematics, MDPI, vol. 11(6), pages 1-26, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1553-:d:1104499
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