The Minimal Total Irregularity of Some Classes of Graphs
In [1], Abdo and Dimitov defined the total irregularity of a graph G = (V, E) as irr t ( G ) = 1 2 ∑ u , v ∈ V | d G ( u ) − d G ( v ) | , where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the mini...
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| Veröffentlicht in: | Filomat 2016-01, Vol.30 (5), p.1203-1211 |
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| creator | Zhu, Yingxue You, Lihua Yang, Jieshan |
| description | In [1], Abdo and Dimitov defined the total irregularity of a graph G = (V, E) as
irr
t
(
G
)
=
1
2
∑
u
,
v
∈
V
|
d
G
(
u
)
−
d
G
(
v
)
|
,
where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research. |
| doi_str_mv | 10.2298/FIL1605203Z |
| format | Article |
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irr
t
(
G
)
=
1
2
∑
u
,
v
∈
V
|
d
G
(
u
)
−
d
G
(
v
)
|
,
where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.</description><identifier>ISSN: 0354-5180</identifier><identifier>EISSN: 2406-0933</identifier><identifier>DOI: 10.2298/FIL1605203Z</identifier><language>eng</language><publisher>Faculty of Sciences and Mathematics, University of Niš</publisher><subject>Vertices</subject><ispartof>Filomat, 2016-01, Vol.30 (5), p.1203-1211</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c292t-22532fdf594827b3ec7e946025485e44ef9b9e801200d00413394beae90af1583</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24898695$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24898695$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,4010,27900,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Zhu, Yingxue</creatorcontrib><creatorcontrib>You, Lihua</creatorcontrib><creatorcontrib>Yang, Jieshan</creatorcontrib><title>The Minimal Total Irregularity of Some Classes of Graphs</title><title>Filomat</title><description>In [1], Abdo and Dimitov defined the total irregularity of a graph G = (V, E) as
irr
t
(
G
)
=
1
2
∑
u
,
v
∈
V
|
d
G
(
u
)
−
d
G
(
v
)
|
,
where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.</description><subject>Vertices</subject><issn>0354-5180</issn><issn>2406-0933</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNpNj0FLw0AUhBdRMFZPnoXcJfr27W6ye5Rg20BKD8aLl7BJ39qU1JTdeOi_N6UiXmYY-BhmGLvn8IRo9PO8KHkKCkF8XLAIJaQJGCEuWQRCyURxDdfsJoQdgMRUZhHT1ZbiVffV7W0fV8M4aeE9fX731nfjMR5c_DbsKc57GwKFU154e9iGW3blbB_o7tdn7H3-WuXLpFwvivylTFo0OCaISqDbOGWkxqwR1GZkZAqopFYkJTnTGNLAEWAzreJCGNmQJQPWcaXFjD2ee1s_hODJ1Qc_jfXHmkN9Ol3_Oz3RD2d6F8bB_6EotdGpUeIHcRBRXg</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Zhu, Yingxue</creator><creator>You, Lihua</creator><creator>Yang, Jieshan</creator><general>Faculty of Sciences and Mathematics, University of Niš</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160101</creationdate><title>The Minimal Total Irregularity of Some Classes of Graphs</title><author>Zhu, Yingxue ; You, Lihua ; Yang, Jieshan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c292t-22532fdf594827b3ec7e946025485e44ef9b9e801200d00413394beae90af1583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhu, Yingxue</creatorcontrib><creatorcontrib>You, Lihua</creatorcontrib><creatorcontrib>Yang, Jieshan</creatorcontrib><collection>CrossRef</collection><jtitle>Filomat</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhu, Yingxue</au><au>You, Lihua</au><au>Yang, Jieshan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Minimal Total Irregularity of Some Classes of Graphs</atitle><jtitle>Filomat</jtitle><date>2016-01-01</date><risdate>2016</risdate><volume>30</volume><issue>5</issue><spage>1203</spage><epage>1211</epage><pages>1203-1211</pages><issn>0354-5180</issn><eissn>2406-0933</eissn><abstract>In [1], Abdo and Dimitov defined the total irregularity of a graph G = (V, E) as
irr
t
(
G
)
=
1
2
∑
u
,
v
∈
V
|
d
G
(
u
)
−
d
G
(
v
)
|
,
where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.</abstract><pub>Faculty of Sciences and Mathematics, University of Niš</pub><doi>10.2298/FIL1605203Z</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 0354-5180 2406-0933 |
| language | eng |
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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics |
| subjects | Vertices |
| title | The Minimal Total Irregularity of Some Classes of Graphs |
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