Class of crosscap two graphs arising from lattices-Ⅱ

Jehan A. Al-Bar; T. Asir; K. Mano; Wafaa M. Fakieh; Jehan A. Al-Bar; T. Asir; K. Mano; Wafaa M. Fakieh

doi:10.3934/math.20231265

AIMS Mathematics

2023, Volume 8, Issue 10: 24802-24824. doi: 10.3934/math.20231265

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Class of crosscap two graphs arising from lattices-Ⅱ

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21461, Saudia Arabia
2.
Department of Mathematics, Pondicherry University, Pondicherry 605014, India
3.
Department of Mathematics, Fatima College, Madurai 625018, Tamil Nadu, India

Received: 10 May 2023 Revised: 26 July 2023 Accepted: 03 August 2023 Published: 23 August 2023
MSC : Primary: 05C75, 05C10, 05C25; Secondary: 06A07, 06B99

In this series of papers, we study the crosscap two embedding of a class of multipartite graphs, namely, annihilating-ideal graphs of a lattice. In Part 1 of the series [Class of crosscap two graphs arising from lattices-Ⅰ, Mathematics, 11 (2023), 1-26], we classified lattices with the number of atoms less than or equal to 4, whose annihilating-ideal graph can be embedded in the Klein bottle. In this paper, which is Part 2 of the series, we classify all finite lattices with at least 5 atoms whose annihilating-ideal graph is embedded in crosscap two surfaces. These characterizations help us to identify classes of multipartite graphs, which are embedded in the Klein bottle.
- atom of a lattice,
- multipartite graphs,
- Klein bottle,
- crosscap,
- annihilating-ideal graph
Citation: Jehan A. Al-Bar, T. Asir, K. Mano, Wafaa M. Fakieh. Class of crosscap two graphs arising from lattices-Ⅱ[J]. AIMS Mathematics, 2023, 8(10): 24802-24824. doi: 10.3934/math.20231265

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Abstract

In this series of papers, we study the crosscap two embedding of a class of multipartite graphs, namely, annihilating-ideal graphs of a lattice. In Part 1 of the series [Class of crosscap two graphs arising from lattices-Ⅰ, Mathematics, 11 (2023), 1-26], we classified lattices with the number of atoms less than or equal to 4, whose annihilating-ideal graph can be embedded in the Klein bottle. In this paper, which is Part 2 of the series, we classify all finite lattices with at least 5 atoms whose annihilating-ideal graph is embedded in crosscap two surfaces. These characterizations help us to identify classes of multipartite graphs, which are embedded in the Klein bottle.

References

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