Another look at the degree-Kirchhoff index

Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i < jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is...

Full description

Saved in:
Bibliographic Details
Published in:International journal of quantum chemistry 2011-11, Vol.111 (14), p.3453-3455
Main Authors: Palacios, José Luis, Renom, José Miguel
Format: Article
Language:English
Subjects:
Kirchhoff index
star graph
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413
cites cdi_FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413
container_end_page 3455
container_issue 14
container_start_page 3453
container_title International journal of quantum chemistry
container_volume 111
creator Palacios, José Luis
Renom, José Miguel
description Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i < jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N2 − 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011
doi_str_mv 10.1002/qua.22725
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_qua_22725</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>QUA22725</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413</originalsourceid><addsrcrecordid>eNp1j11PgzAUhhujiTi98B9wq0m3FmhLL8mi00n8SJzjrmnpQXA4XMG4_XtR1Duvzjl5n_ckD0KnlIwpIcFk867HQSACtoc8SqTAEafZPvL6jGDBSXyIjtr2hRDCQy48dJ6sm64E59dNs_J15_eHb-HZAeCbyuVl2RSFX60tbI_RQaHrFk5-5ggtLi8ep1c4vZtdT5MU5yERDIdGggCjuQVJaSGtNMway4TQcSwhN0zy2EJEcxkDUGJkFEc57VejCxHRcITOhr-5a9rWQaHeXPWq3U5Ror4kVS-pviV7djKwH1UNu_9B9bBIfht4aFRtB9u_hnYrxUUomFreztTyKZ3Ps_tIZeEnWFNirA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Another look at the degree-Kirchhoff index</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Palacios, José Luis ; Renom, José Miguel</creator><creatorcontrib>Palacios, José Luis ; Renom, José Miguel</creatorcontrib><description>Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i &lt; jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N2 − 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011</description><identifier>ISSN: 0020-7608</identifier><identifier>EISSN: 1097-461X</identifier><identifier>DOI: 10.1002/qua.22725</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc., A Wiley Company</publisher><subject>Kirchhoff index ; star graph</subject><ispartof>International journal of quantum chemistry, 2011-11, Vol.111 (14), p.3453-3455</ispartof><rights>Copyright © 2010 Wiley Periodicals, Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413</citedby><cites>FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27907,27908</link.rule.ids></links><search><creatorcontrib>Palacios, José Luis</creatorcontrib><creatorcontrib>Renom, José Miguel</creatorcontrib><title>Another look at the degree-Kirchhoff index</title><title>International journal of quantum chemistry</title><addtitle>Int. J. Quantum Chem</addtitle><description>Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i &lt; jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N2 − 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011</description><subject>Kirchhoff index</subject><subject>star graph</subject><issn>0020-7608</issn><issn>1097-461X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1j11PgzAUhhujiTi98B9wq0m3FmhLL8mi00n8SJzjrmnpQXA4XMG4_XtR1Duvzjl5n_ckD0KnlIwpIcFk867HQSACtoc8SqTAEafZPvL6jGDBSXyIjtr2hRDCQy48dJ6sm64E59dNs_J15_eHb-HZAeCbyuVl2RSFX60tbI_RQaHrFk5-5ggtLi8ep1c4vZtdT5MU5yERDIdGggCjuQVJaSGtNMway4TQcSwhN0zy2EJEcxkDUGJkFEc57VejCxHRcITOhr-5a9rWQaHeXPWq3U5Ror4kVS-pviV7djKwH1UNu_9B9bBIfht4aFRtB9u_hnYrxUUomFreztTyKZ3Ps_tIZeEnWFNirA</recordid><startdate>20111115</startdate><enddate>20111115</enddate><creator>Palacios, José Luis</creator><creator>Renom, José Miguel</creator><general>Wiley Subscription Services, Inc., A Wiley Company</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20111115</creationdate><title>Another look at the degree-Kirchhoff index</title><author>Palacios, José Luis ; Renom, José Miguel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Kirchhoff index</topic><topic>star graph</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Palacios, José Luis</creatorcontrib><creatorcontrib>Renom, José Miguel</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>International journal of quantum chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Palacios, José Luis</au><au>Renom, José Miguel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Another look at the degree-Kirchhoff index</atitle><jtitle>International journal of quantum chemistry</jtitle><addtitle>Int. J. Quantum Chem</addtitle><date>2011-11-15</date><risdate>2011</risdate><volume>111</volume><issue>14</issue><spage>3453</spage><epage>3455</epage><pages>3453-3455</pages><issn>0020-7608</issn><eissn>1097-461X</eissn><abstract>Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i &lt; jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N2 − 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc., A Wiley Company</pub><doi>10.1002/qua.22725</doi><tpages>3</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0020-7608
ispartof International journal of quantum chemistry, 2011-11, Vol.111 (14), p.3453-3455
issn 0020-7608
1097-461X
language eng
recordid cdi_crossref_primary_10_1002_qua_22725
source Wiley-Blackwell Read & Publish Collection
subjects Kirchhoff index
star graph
title Another look at the degree-Kirchhoff index
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-17T03%3A00%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Another%20look%20at%20the%20degree-Kirchhoff%20index&rft.jtitle=International%20journal%20of%20quantum%20chemistry&rft.au=Palacios,%20Jos%C3%A9%20Luis&rft.date=2011-11-15&rft.volume=111&rft.issue=14&rft.spage=3453&rft.epage=3455&rft.pages=3453-3455&rft.issn=0020-7608&rft.eissn=1097-461X&rft_id=info:doi/10.1002/qua.22725&rft_dat=%3Cwiley_cross%3EQUA22725%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c3075-3b9e7eba6de911f9d9b5dbd577a889ecb5968de41c98ee10b9484c1ee1baf7413%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true