The Structure of Tripotent Graph of Certain Commutative Rings
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107-114Keywords:
Abstract
In this paper, we characterize the texture of tripotent graph of the ring, which is associated by tripotent element of a ring such that, for every two distinct vertices; and then, their adjacent if and only if. We establish several structural graphical properties of tripotent graph of local ring when it is a path graph and it is spanning subgraph with unit graph and clean graph. Also, we obtain that, the tripotent graph is Hamiltonian graph but doesn't Eulerian. Moreover, we investigate the concept of tripotent graph of a commutative ring where and for is a prime integer as , and which equals to . Furthermore, we prove that the tripotent graph of commutative ring is 4-partite graph and , for . Finally, we are concerned about the metric dimension of tripotent graph of some cases of commutative rings, especially; where tripotent graphs are planar and nonplanar.
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This work is licensed under a Creative Commons Attribution 4.0 International License.
