Open Access
Vimal Patel
Dr. Suresh Sorathia
Dr. Amit Rokad
- Research Scholar Mathematics Dept., Surendranagar, University Gujarat India
- Associate Professor Mathematics Dept., Surendranagar, University Gujarat
- Assistant Professor Mathematics Dept., M.G.Science Institute, Ahmedabad Gujarat India
Abstract
The function φ: V (G) → {F1, F2,…, Fn}, where Fj is the jth Fibonacci number (j = 1,…, n), is said to be Fibonacci product cordial labeling if the induced function φ*: E (G) → {0, 1} defined by 𝜑∗ (𝑢𝑣) = (𝜑(𝑢)𝜑 (𝑣))(𝑚𝑜𝑑 2) meets the criterion |𝑒𝜑∗(0) – � �𝜑∗(1)| ≤ 1. A graph known as the Fibonacci product cordial graph is one that permits Fibonacci product cordial labeling. The abstract summarizes a research paper that extends the study of cordial labeling to include Fibonacci product cordial labeling, focusing on the Herschel graph and its behavior under various graph operations. The Fibonacci product cordial labeling of the Herschel graph and several graph operations on it were examined in this work.
We established the following findings in this paper:
(1). The Herschel graph Hs is a Fibonacci product cordial graph.
(2). In a Herschel graph, a Fibonacci product cordial network is formed by fusing any
two neighboring vertices of degree
(3). Herschel graphs are Fibonacci product cordial graphs when any vertex in the graph
is duplicated.
(4). The switching of a central vertex v in the Herschel graph Hs is a Fibonacci product
cordial graph.
(5). The graph obtained by joint of two copies of Herschel graph Hs is a Fibonacci
product cordial graph.
(6). DS(Hs) is Fibonacci product cordial graph.
Keywords: Productcordiallabeling,fusion, duplication, switching, joint sum, degree splitting
[This article belongs to Research & Reviews: Discrete Mathematical Structures(rrdms)]
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Research & Reviews: Discrete Mathematical Structures
| Volume | 11 |
| Issue | 01 |
| Received | April 16, 2024 |
| Accepted | June 29, 2024 |
| Published | July 8, 2024 |