Some results on the strongly annihilator ideal graph of a lattice

Articles in Press

Document Type : Original paper

Authors

1 Department of Applied science and humanities, School of engineering and sciences, MIT Art, Design and Technology University, Pune-412 201, India

2 Department of Mathematics, Abasaheb Garware College, Pune-411 004, India

Abstract

For a lattice L, the strongly annihilator ideal graph of L is denoted by SAnnIG(L). It is a graph with the vertex set, which consists of all ideals in L that have nontrivial annihilators such that any two distinct vertices I and J are adjacent in SAnnIG(L) if and only if the annihilator of I contains a nonzero element of J and the annihilator of J contains a nonzero element of I. In this paper, we determine the radius, circumference, and domination number of SAnnIG(L). We obtain necessary and sufficient conditions for SAnnIG(L) to be in the class of paths, cycles, unicyclic, triangle-free, trees, complete multipartite, split or claw-free graphs. Among other results, we study the affinity between the strongly annihilator ideal and the annihilator ideal graph of a lattice.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 13 February 2025

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