### Indeks Harmonik dan Indeks Gutman Graf Nilradikal pada Gelanggang Komutatif dengan Satuan

Luluk Afifah, Imam Sujarwo, Muhammad Khudzaifah

#### Abstract

Graph theory is a topic that is still an important subject to discuss. This is because until now graph theory has many practical applications in various disciplines, for example in biology, computer science, economics, informatics engineering, linguistics, mathematics, health, and social sciences. This study discusses the Gutman index of nilradical graphs in the commutative ring with unity.
A nilradical graph whose vertices are non-zero nilpotent elements, when the domain is a commutative ring with units, it forms a complete graph only if the commutative ring with units we use is limited to a positive integer modulo n (Z_n). Where n is the square of the prime number p which is less than equal to 3. It is known that the general pattern of harmonic indices and Gutman indices of nilradical graphs in the commutative ring with unity are H(N(Z_(n=p^2 ) ))=((p-2)^2+(p -2))/2(p-2) and Gut(N(Z_(n=p^2 ) ))=(1/2 ((p-2)^2+(p-2))) (p- 2)^2 respectively. In its application, this general form can be used as a numerical parameter of a graph in chemical graph theory, molecular topology, and mathematical chemistry.

#### Keywords

Harmonic Indeks; Gutman Index; Complete Graph; Nilradical Graph

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#### References

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DOI: https://doi.org/10.18860/jrmm.v2i4.14902

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