Journals Information
Mathematics and Statistics Vol. 13(4), pp. 232 - 236
DOI: 10.13189/ms.2025.130407
Reprint (PDF) (1454Kb)
Generalized Composition of Cycle and Path Graphs
Akhil B. 1,*, Roy John 2, Manju V. N. 1, Athira Chandran 1
1 Department of Mathematics, University of Kerala, Karyavattom, Thiruvananthapuram, 695581, Kerala, India
2 Department of Mathematics, St. Stephen's College, Pathanapuram, Kollam, 689695, Kerala, India
ABSTRACT
In this article, we explore the significance of graph operations, which provide a versatile framework for modeling, analyzing, and solving complex problems involving relationships and connections between entities. These operations are fundamental across various fields and play a vital role in advancing research, technology, and decision-making. Commonly used graph operations include composition, tensor product, and Cartesian product. In addition to these, several new variations have been introduced in recent literature. We begin by presenting these operations and then consider their generalizations, which can be approached either parametrically or structurally鈥攖hat is, by generalizing the graph structure itself or the parameters involved in the operations. In particular, this article focuses on the generalized composition, known as the 
-composition, of cycle and path-related graphs. This generalization is based on the parameter distance between vertices. Since the standard composition of graphs does not necessarily preserve connectedness, we examine results related to the connectedness of graphs under this generalized composition. For suitable values of , we derive graphs resulting from the generalized composition of cycles and paths. These resulting graphs may be isomorphic, non-isomorphic, or consist of a single connected component. Furthermore, we identify a class of graphs for which the commutativity property holds under this generalized composition for certain values of .
KEYWORDS
-composition, Cycle, Path, Isomorphism, Connected Graphs, Regular Graphs
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akhil B. , Roy John , Manju V. N. , Athira Chandran , "Generalized Composition of Cycle and Path Graphs," Mathematics and Statistics, Vol. 13, No. 4, pp. 232 - 236, 2025. DOI: 10.13189/ms.2025.130407.
(b). APA Format:
Akhil B. , Roy John , Manju V. N. , Athira Chandran (2025). Generalized Composition of Cycle and Path Graphs. Mathematics and Statistics, 13(4), 232 - 236. DOI: 10.13189/ms.2025.130407.