Peripheral Wiener index of a graph
The {\em eccentricity} of a vertex $v$ is the maximum distance between $v$ and any other vertex. A vertex with maximum eccentricity is called a peripheral vertex. The peripheral Wiener index $PW(G)$ of a graph $G$ is defined as the sum of the distances between all pairs of peripheral vertices...
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| Format: | Article |
| Language: | English |
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Azarbaijan Shahide Madani University
2017-01-01
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| Series: | Communications in Combinatorics and Optimization |
| Subjects: | |
| Online Access: | http://comb-opt.azaruniv.ac.ir/article_13596.html |
| _version_ | 1818513799404060672 |
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| author | K.P. Narayankar S.B. Lokesh |
| author_facet | K.P. Narayankar S.B. Lokesh |
| author_sort | K.P. Narayankar |
| collection | DOAJ |
| description | The {\em eccentricity} of a vertex $v$ is the maximum distance between $v$ and any other vertex. A vertex with maximum eccentricity is called a peripheral vertex. The peripheral Wiener index $PW(G)$ of a graph $G$ is
defined as the sum of the distances between all pairs of peripheral vertices of $G$.
In this paper, we initiate the study of the peripheral Wiener index and investigate
its basic properties. In particular, we determine the peripheral
Wiener index of the cartesian product of two graphs and trees. |
| first_indexed | 2024-12-11T00:06:32Z |
| format | Article |
| id | doaj.art-f873b2473cef41c2be659dd31d5b6977 |
| institution | Directory Open Access Journal |
| issn | 2538-2128 2538-2136 |
| language | English |
| last_indexed | 2024-12-11T00:06:32Z |
| publishDate | 2017-01-01 |
| publisher | Azarbaijan Shahide Madani University |
| record_format | Article |
| series | Communications in Combinatorics and Optimization |
| spelling | doaj.art-f873b2473cef41c2be659dd31d5b69772022-12-22T01:28:19ZengAzarbaijan Shahide Madani UniversityCommunications in Combinatorics and Optimization2538-21282538-21362017-01-0121435610.22049/CCO.2017.13596Peripheral Wiener index of a graphK.P. Narayankar0S.B. Lokesh1Department of Mathematics, Mangalore University, Mangalagangothri, Mangalore-574199, IndiaDepartment of Mathematics, Mangalore University, Mangalagangothri, Mangalore-574199, IndiaThe {\em eccentricity} of a vertex $v$ is the maximum distance between $v$ and any other vertex. A vertex with maximum eccentricity is called a peripheral vertex. The peripheral Wiener index $PW(G)$ of a graph $G$ is defined as the sum of the distances between all pairs of peripheral vertices of $G$. In this paper, we initiate the study of the peripheral Wiener index and investigate its basic properties. In particular, we determine the peripheral Wiener index of the cartesian product of two graphs and trees.http://comb-opt.azaruniv.ac.ir/article_13596.htmlDistance in graphsWiener indexperipheral Wiener index |
| spellingShingle | K.P. Narayankar S.B. Lokesh Peripheral Wiener index of a graph Communications in Combinatorics and Optimization Distance in graphs Wiener index peripheral Wiener index |
| title | Peripheral Wiener index of a graph |
| title_full | Peripheral Wiener index of a graph |
| title_fullStr | Peripheral Wiener index of a graph |
| title_full_unstemmed | Peripheral Wiener index of a graph |
| title_short | Peripheral Wiener index of a graph |
| title_sort | peripheral wiener index of a graph |
| topic | Distance in graphs Wiener index peripheral Wiener index |
| url | http://comb-opt.azaruniv.ac.ir/article_13596.html |
| work_keys_str_mv | AT kpnarayankar peripheralwienerindexofagraph AT sblokesh peripheralwienerindexofagraph |