Dimensi Partisi Dominasi Graf Kelas Pohon
DOI:
https://doi.org/10.24252/msa.v13i1.60746Keywords:
pohon, dimensi graf, partisi pembeda, partisi dominasiAbstract
Dimensi partisi dominasi merupakan konsep yang menggabungkan dua ide penting dalam teori graf: partisi pembeda dan himpunan dominasi. Misalkan G adalah suatu graf terhubung dan Γ={L-1, L_2, . . . , L_k} adalah partisi terurut dari himpunan titik graf G. Suatu partisi Γ disebut partisi pembeda jika untuk setiap sepasang titik u dan v , jarak antara u dan L_j tidak sama dengan jarak v dan L_j untuk suatu L_j ϵ Γ. Suatu partisi pembeda Γ dikatakan partisi pembeda dominasi jika untuk setiap titik u di G jarak antara titik u dan suatu kelas partisi L_j adalah satu. Selanjutnya, dimensi partisi graf G adalah kardinalitas minimum dari suatu partisi pembeda dari G . Adapun kardinalitas minimum dari suatu partisi pembeda dominasi dari G disebut dimensi partisi dominasi. Sebagai pengembangan penelitian dalam kajian dimensi partisi dominasi, dalam makalah ini dikaji dimensi partisi dominasi graf dalam kelas pohon. Hasil dari penelitian ini menunjukkan dimensi partisi dominasi untuk graf bintang ganda, graf ulat, graf kembang api, dan graf pohon pisang.
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