A theoretical analysis of Hyper-Wiener indices in graphs derived from algebraic structures

Ashadul Umam; Abdurahim

Penulis

Ashadul Umam Departement of Mathematics, University of Mataram Penulis
Abdurahim Departement of Mathematics, University of Mataram Penulis

Kata Kunci:

Hyper-Wiener, Graf Non-coprime, Graf Kuasa, Graf Coprime, Grup Modulo, Grup Dihedral

Abstrak

Indeks Hyper-Wiener adalah deskriptor topologi yang banyak digunakan untuk mengkuantifikasi kompleksitas struktural graf, terutama yang muncul dari struktur aljabar. Tulisan ini menyajikan sintesis terstruktur dari teorema-teorema kunci terkait indeks Hyper-Wiener dalam graf koprima, graf non-koprima, dan graf pangkat yang dibangun dari grup modulo integer dan grup dihedral. Dengan menggunakan pendekatan tinjauan pustaka sistematis, kami menyusun dan menyajikan kembali hasil-hasil formal, termasuk rumus-rumus eksplisit dan sifat-sifat yang telah terbukti. Setiap teorema dianalisis dalam kaitannya dengan struktur aljabar grup yang mendasarinya dan topologi graf yang dihasilkan. Temuan kami menyoroti bagaimana sifat-sifat teori grup—seperti orde, operasi, dan interaksi elemen—berdampak langsung pada indeks Hyper-Wiener. Tulisan ini dimaksudkan untuk mendukung para peneliti dengan menyediakan jembatan konseptual antara teori grup dan teori graf topologi, serta dengan mengidentifikasi arah potensial untuk penelitian di masa mendatang.

Unduhan

Data unduhan tidak tersedia.

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