An induced P3-packing k-partition number for Benzenoid System

Authors

Santiagu Theresal
Department of Mathematics, Auxilium College of Arts and Science for Women
S. Arul Amirtha Raja
Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai-600 119

Synopsis

A subfield of chemistry known as mathematical chemistry uses mathematical techniques to discuss chemical structures. A chemical graph is the representation of a chemical/molecular structure in terms of a graph, such that each of its atoms is represented by a vertex with an edge representing a bond/multiple bonds between two of its atoms. Such a graph G = (V,E) is simple, undirected, finite, and connected. The order and size of G are, respectively, the number of vertices and edges in it. For the connection of vertex set V (G) and edge set E (G) of a graph, there must be an existence of linking between any pair of vertices in G. A benzenoid system is a combinatorial object obtained by arranging congruent regular hexagons in a plane so that two hexagons are either disjoint or have a common edge. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is the set of vertex disjoint sub graphs of G, each of which is isomorphic to a fixed graph H. In this paper we determine a H-packing and an induced H-packing k-partition number for Rhombic Benzenoid System, triangular benzenoid system and Benzene Ring-Molecular graph of P [m,n] with H ≃P_3. A chemical graph is the representation of a chemical/molecular structure in terms of a graph, such that each of its atoms is represented by a vertex with an edge representing a bond/multiple bonds between two of its atoms. Such a graph  is simple, undirected, finite, and connected. The order and size of G are, respectively, the number of vertices and edges in it. For the connection of vertex set and edge set of a graph, there must be an existence of linking between any pair of vertices in . A benzenoid system is a combinatorial object obtained by arranging congruent regular hexagons in a plane so that two hexagons are either disjoint or have a common edge. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An -packing of a graph  is the set of vertex disjoint sub graphs of , each of which is isomorphic to a fixed graph H. In this paper we determine a -packing and an induced -packing -partition number for Rhombic Benzenoid System, triangular benzenoid system and Benzene Ring-Molecular graph of ] with .

ICRTMCS-2023
Published
October 19, 2023