Nilai ketakteraturan refleksif sisi pada graf hasil kali corona antara graf ular persegi terbuka kiri (OL(SS_n)) dengan graf kosong (N_m)

Rojab, Septian Abdul (2025) Nilai ketakteraturan refleksif sisi pada graf hasil kali corona antara graf ular persegi terbuka kiri (OL(SS_n)) dengan graf kosong (N_m). Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Indonesia: Pelabelan graf merupakan topik yang menarik dalam teori graf, karena penelitiannya terus berkembang sampai saat ini. Pada tahun 2017, Dushyant Tanna, Joe Ryan, dan Andrea Semaničová-Feňovčíková mengkaji pelabelan-\textit{k} refleksif tak teratur sisi pada suatu graf $G$. Pelabelan refleksif tak teratur sisi dari suatu graf $G$ didefinisikan memiliki pelabelan sisi $\varphi_e:E(G) \to \{1,2,\cdots,k_e \}$ dan pelabelan titik $\varphi_v:V(G) \to \{0,2, \cdots,2k_v \}$, sehingga untuk setiap dua sisi berbeda $xy$ dan $x'y'$ terdapat $wt(xy) \neq wt(x'y')$ di mana $wt(xy) = \varphi_v (x) + \varphi_e (xy) + \varphi_v (y)$ dan $wt(x'y')= \varphi_v (x') + \varphi_e (x'y') + \varphi_v (y')$. Nilai $k$ terkecil di mana $k = maks\{k_v, 2k_e\}$ sehingga $G$ memiliki pelabelan-$k$ disebut nilai ketakteraturan refleksif sisi dari $G$ dinotasikan dengan $res(G)$. Pada penelitian ini ditentukan nilai ketakteraturan refleksif sisi pada graf hasil kali corona antara graf ular persegi terbuka kiri $(OL(SS_n))$ dengan graf kosong $(N_m)$. Inggris: Graph labeling is an intriguing topic in graph theory, as research in this area continues to evolve to this day. In 2017, Dushyant Tanna, Joe Ryan, and Andrea Semaničová-Feňovčíková investigated the edge-reflexive irregular \( k \)-labeling of a graph \( G \). An edge-reflexive irregular labeling of a graph \( G \) is defined as having an edge labeling \( \varphi_e: E(G) \to \{1, 2, \dots, k_e\} \) and a vertex labeling \( \varphi_v: V(G) \to \{0, 2, \dots, 2k_v\} \), such that for any two distinct edges \( xy \) and \( x'y' \), the condition \( wt(xy) \neq wt(x'y') \) holds, where \( wt(xy) = \varphi_v(x) + \varphi_e(xy) + \varphi_v(y) \) and \( wt(x'y') = \varphi_v(x') + \varphi_e(x'y') + \varphi_v(y') \). The smallest value of \( k \), where \( k = \max\{k_v, 2k_e\} \), for which \( G \) admits a \( k \)-labeling, is called the edge-reflexive irregularity strength of \( G \), denoted by \( \text{res}(G) \). In this research, we determine the edge-reflexive irregularity strength of the corona product graph between a open left square snake graph \( (OL(SS_n)) \) and null graph \( (N_m) \).

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