The energy of some tree dendrimers
The concept of energy of a graph was first introduced by I. Gutman [ 5 ] in 1978. The energy E ( G ) of a simple graph G is defined to be the sum of the absolute values of the eigenvalues of G . The tree dendrimer d ( n , k ) is a finite connected cycle free graph, also known as Bethe lattice. The...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2022-04, Vol.68 (2), p.1033-1045 |
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| creator | Bokhary, Syed Ahtsham Ul Haq Tabassum, Hafsah |
| description | The concept of energy of a graph was first introduced by I. Gutman [
5
] in 1978. The
energy
E
(
G
) of a simple graph
G
is defined to be the sum of the absolute values of the eigenvalues of
G
. The tree dendrimer
d
(
n
,
k
) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in
d
(
n
,
k
) is connected to
(
k
-
1
)
. It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of
d
(2,
k
) and
d
(3,
k
) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of
n
and
k
is also given. |
| doi_str_mv | 10.1007/s12190-021-01531-y |
| format | Article |
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5
] in 1978. The
energy
E
(
G
) of a simple graph
G
is defined to be the sum of the absolute values of the eigenvalues of
G
. The tree dendrimer
d
(
n
,
k
) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in
d
(
n
,
k
) is connected to
(
k
-
1
)
. It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of
d
(2,
k
) and
d
(3,
k
) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of
n
and
k
is also given.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-021-01531-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Apexes ; Applied mathematics ; Computational Mathematics and Numerical Analysis ; Dendrimers ; Eigenvalues ; Mathematical and Computational Engineering ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Original Research ; Polynomials ; Reduction ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2022-04, Vol.68 (2), p.1033-1045</ispartof><rights>Korean Society for Informatics and Computational Applied Mathematics 2021</rights><rights>Korean Society for Informatics and Computational Applied Mathematics 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-fbd730434525c29450ff3e56eaeb420a937a3bf3be655a561e7dfe7b5cb7f69e3</citedby><cites>FETCH-LOGICAL-c319t-fbd730434525c29450ff3e56eaeb420a937a3bf3be655a561e7dfe7b5cb7f69e3</cites><orcidid>0000-0002-8957-0792</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12190-021-01531-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-021-01531-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Bokhary, Syed Ahtsham Ul Haq</creatorcontrib><creatorcontrib>Tabassum, Hafsah</creatorcontrib><title>The energy of some tree dendrimers</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>The concept of energy of a graph was first introduced by I. Gutman [
5
] in 1978. The
energy
E
(
G
) of a simple graph
G
is defined to be the sum of the absolute values of the eigenvalues of
G
. The tree dendrimer
d
(
n
,
k
) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in
d
(
n
,
k
) is connected to
(
k
-
1
)
. It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of
d
(2,
k
) and
d
(3,
k
) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of
n
and
k
is also given.</description><subject>Apexes</subject><subject>Applied mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Dendrimers</subject><subject>Eigenvalues</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Original Research</subject><subject>Polynomials</subject><subject>Reduction</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWKtfwNOi5-gk2UmaoxT_QcFLPYdkd1Itdrcm28N-e6MrePM0w_Dem8ePsUsBNwLA3GYhhQUOUnAQqAQfj9hMLDRyCQs8LjvaBcdyOGVnOW8BtLFgZ-xq_UYVdZQ2Y9XHKvc7qoZEVLXUtel9Rymfs5PoPzJd_M45e324Xy-f-Orl8Xl5t-KNEnbgMbRGQa1qlNhIWyPEqAg1eQq1BG-V8SpEFUgjetSCTBvJBGyCidqSmrPrKXef-s8D5cFt-0PqyksndQ2I1lhdVHJSNanPOVF0-1LTp9EJcN8s3MTCFRbuh4Ubi0lNplzE3YbSX_Q_ri_AvWDV</recordid><startdate>20220401</startdate><enddate>20220401</enddate><creator>Bokhary, Syed Ahtsham Ul Haq</creator><creator>Tabassum, Hafsah</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-8957-0792</orcidid></search><sort><creationdate>20220401</creationdate><title>The energy of some tree dendrimers</title><author>Bokhary, Syed Ahtsham Ul Haq ; Tabassum, Hafsah</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-fbd730434525c29450ff3e56eaeb420a937a3bf3be655a561e7dfe7b5cb7f69e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Apexes</topic><topic>Applied mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Dendrimers</topic><topic>Eigenvalues</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Original Research</topic><topic>Polynomials</topic><topic>Reduction</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bokhary, Syed Ahtsham Ul Haq</creatorcontrib><creatorcontrib>Tabassum, Hafsah</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bokhary, Syed Ahtsham Ul Haq</au><au>Tabassum, Hafsah</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The energy of some tree dendrimers</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2022-04-01</date><risdate>2022</risdate><volume>68</volume><issue>2</issue><spage>1033</spage><epage>1045</epage><pages>1033-1045</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>The concept of energy of a graph was first introduced by I. Gutman [
5
] in 1978. The
energy
E
(
G
) of a simple graph
G
is defined to be the sum of the absolute values of the eigenvalues of
G
. The tree dendrimer
d
(
n
,
k
) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in
d
(
n
,
k
) is connected to
(
k
-
1
)
. It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of
d
(2,
k
) and
d
(3,
k
) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of
n
and
k
is also given.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s12190-021-01531-y</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0002-8957-0792</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1598-5865 |
| ispartof | Journal of applied mathematics & computing, 2022-04, Vol.68 (2), p.1033-1045 |
| issn | 1598-5865 1865-2085 |
| language | eng |
| recordid | cdi_proquest_journals_2640559796 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Apexes Applied mathematics Computational Mathematics and Numerical Analysis Dendrimers Eigenvalues Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Original Research Polynomials Reduction Theory of Computation |
| title | The energy of some tree dendrimers |
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