Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1)
Let be a graph with vertex set . The number of vertices in is the order of and is denoted by . The connected hub polynomial of Gdenoted by is defined as where denotes the number of connected hub sets of of cardinality and denotes the connected hub number of .Let denotes the Lollipop graph wi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Piceno Aprutina dei Velati
2022-12-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/886 |
| _version_ | 1811302259086065664 |
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| author | T Anggelinshiny Baby Anitha |
| author_facet | T Anggelinshiny Baby Anitha |
| author_sort | T Anggelinshiny |
| collection | DOAJ |
| description | Let be a graph with vertex set . The number of vertices in is the order of and is denoted by . The connected hub polynomial of Gdenoted by is defined as where denotes the number of connected hub sets of of cardinality and denotes the connected hub number of .Let denotes the Lollipop graph with vertices. The connected hub polynomial of denoted by is defined as,where denotes the number of connected hub sets of of cardinality , and denotes the connected hub number of .In this paper, we derive a recursive formula for . From this recursive formula, we construct the connected hub polynomial of as,Also we study some properties of this polynomial |
| first_indexed | 2024-04-13T07:24:51Z |
| format | Article |
| id | doaj.art-84dfb1c50086422c9454ec249b711291 |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-04-13T07:24:51Z |
| publishDate | 2022-12-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-84dfb1c50086422c9454ec249b7112912022-12-22T02:56:31ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142022-12-01440293510.23755/rm.v44i0.886676Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1)T Anggelinshiny0Baby Anitha1Research Scholar (Reg. No. 20213282092009), Department of Mathematics, Women’s Christian College, Nagercoil, Tamil Nadu, India. Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012Assistant Professor, Department of Mathematics, Women’s Christian College, Nagercoil, Tamil Nadu, India. Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012Let be a graph with vertex set . The number of vertices in is the order of and is denoted by . The connected hub polynomial of Gdenoted by is defined as where denotes the number of connected hub sets of of cardinality and denotes the connected hub number of .Let denotes the Lollipop graph with vertices. The connected hub polynomial of denoted by is defined as,where denotes the number of connected hub sets of of cardinality , and denotes the connected hub number of .In this paper, we derive a recursive formula for . From this recursive formula, we construct the connected hub polynomial of as,Also we study some properties of this polynomialhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/886lollipop graph, connected hub set, connected hub number, connected hub polynomial |
| spellingShingle | T Anggelinshiny Baby Anitha Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) Ratio Mathematica lollipop graph, connected hub set, connected hub number, connected hub polynomial |
| title | Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) |
| title_full | Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) |
| title_fullStr | Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) |
| title_full_unstemmed | Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) |
| title_short | Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1) |
| title_sort | connected hub sets and connected hub polynomials of the lollipop graph l p 1 |
| topic | lollipop graph, connected hub set, connected hub number, connected hub polynomial |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/886 |
| work_keys_str_mv | AT tanggelinshiny connectedhubsetsandconnectedhubpolynomialsofthelollipopgraphlp1 AT babyanitha connectedhubsetsandconnectedhubpolynomialsofthelollipopgraphlp1 |