Class of Crosscap Two Graphs Arising from Lattices–I

T. Asir (), K. Mano, Jehan A. Al-Bar and Wafaa M. Fakieh
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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

Mathematics, 2023, vol. 11, issue 6, 1-26

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.

Keywords: crosscap; Klein bottle; lattice; annihilating-ideal graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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