The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

The Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G. In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and di...

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Main Authors: Kun Zhao, Shangzhao Li, Shaojun Dai
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/6680242
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spelling doaj-309b3ce0514c44d48cfad52d54c6f5972021-04-12T01:23:19ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/6680242The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most FourKun Zhao0Shangzhao Li1Shaojun Dai2Department of MathematicsSchool of Mathematics and StatisticsSchool of Mathematical SciencesThe Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G. In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.http://dx.doi.org/10.1155/2021/6680242
collection DOAJ
language English
format Article
sources DOAJ
author Kun Zhao
Shangzhao Li
Shaojun Dai
spellingShingle Kun Zhao
Shangzhao Li
Shaojun Dai
The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
Journal of Mathematics
author_facet Kun Zhao
Shangzhao Li
Shaojun Dai
author_sort Kun Zhao
title The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
title_short The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
title_full The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
title_fullStr The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
title_full_unstemmed The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
title_sort minimum merrifield–simmons index of unicyclic graphs with diameter at most four
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description The Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G. In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.
url http://dx.doi.org/10.1155/2021/6680242
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AT shangzhaoli theminimummerrifieldsimmonsindexofunicyclicgraphswithdiameteratmostfour
AT shaojundai theminimummerrifieldsimmonsindexofunicyclicgraphswithdiameteratmostfour
AT kunzhao minimummerrifieldsimmonsindexofunicyclicgraphswithdiameteratmostfour
AT shangzhaoli minimummerrifieldsimmonsindexofunicyclicgraphswithdiameteratmostfour
AT shaojundai minimummerrifieldsimmonsindexofunicyclicgraphswithdiameteratmostfour
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