Open AccessMerrifield-Simmons index of Cartesian product of two graphs
Author(s) -
Man Liu,
Shiping Tian,
Qidong Yang
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1486/7/072073
Subject(s) - cartesian product , graph , mathematics , combinatorics , index (typography) , product (mathematics) , topological index , star (game theory) , cartesian coordinate system , order (exchange) , discrete mathematics , computer science , geometry , mathematical analysis , world wide web , finance , economics
Merrifield-Simmons index of a graph G shorted word M-S index, noted by σ( G ), which is defined as the number of the independent sets of the graph G . In this paper, a special graph is defined and considered the Merrifield-Simmons index. The main concer in this work is devoted to calculating the number of independent sets with respect to the Cartesian product of S m and P n , where S m is a star of order m and P n is a path of order n , respectively.