Eccentric connectivity index and eccentric distance sum of some graph operations
Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $xi^{c}(G)$, is defined as $xi^{c}(G)=sum_{vin V(G)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. The eccentric distance sum of $G$ is defined as $xi^{d}(G)=sum_{vin V(G)}ec(v)D...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2013-03-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | http://www.combinatorics.ir/?_action=showPDF&article=2839&_ob=e28e6997585de2cc61c0727cd04dec50&fileName=full_text.pdf. |
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| author | Buzohragul Eskender Elkin Vumar |
| author_facet | Buzohragul Eskender Elkin Vumar |
| author_sort | Buzohragul Eskender |
| collection | DOAJ |
| description | Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $xi^{c}(G)$, is defined as $xi^{c}(G)=sum_{vin V(G)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. The eccentric distance sum of $G$ is defined as $xi^{d}(G)=sum_{vin V(G)}ec(v)D(v)$, where $D(v)=sum_{uin V(G)}d_{G}(u,v)$ and $d_{G}(u,v)$ is the distance between $u$ and $v$ in $G$. In this paper, we calculate the eccentric connectivity index and eccentric distance sum of generalized hierarchical product of graphs. Moreover, we present explicit formulae for the eccentric connectivity index of $F$-sum graphs in terms of some invariants of the factors. As applications, we present exact formulae for the values of the eccentric connectivity index of some graphs of chemical interest such as $C_{4}$ nanotubes, $C_{4}$ nanotoris and hexagonal chains. |
| first_indexed | 2024-12-12T14:14:03Z |
| format | Article |
| id | doaj.art-40775eb232084c779d49ab41f22b93a7 |
| institution | Directory Open Access Journal |
| issn | 2251-8657 2251-8665 |
| language | English |
| last_indexed | 2024-12-12T14:14:03Z |
| publishDate | 2013-03-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj.art-40775eb232084c779d49ab41f22b93a72022-12-22T00:21:57ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652013-03-0121103111Eccentric connectivity index and eccentric distance sum of some graph operationsBuzohragul EskenderElkin VumarLet $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $xi^{c}(G)$, is defined as $xi^{c}(G)=sum_{vin V(G)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. The eccentric distance sum of $G$ is defined as $xi^{d}(G)=sum_{vin V(G)}ec(v)D(v)$, where $D(v)=sum_{uin V(G)}d_{G}(u,v)$ and $d_{G}(u,v)$ is the distance between $u$ and $v$ in $G$. In this paper, we calculate the eccentric connectivity index and eccentric distance sum of generalized hierarchical product of graphs. Moreover, we present explicit formulae for the eccentric connectivity index of $F$-sum graphs in terms of some invariants of the factors. As applications, we present exact formulae for the values of the eccentric connectivity index of some graphs of chemical interest such as $C_{4}$ nanotubes, $C_{4}$ nanotoris and hexagonal chains.http://www.combinatorics.ir/?_action=showPDF&article=2839&_ob=e28e6997585de2cc61c0727cd04dec50&fileName=full_text.pdf.Eccentric connectivity indexeccentric distance sumgeneralized hierarchical product$F$-sum graphs |
| spellingShingle | Buzohragul Eskender Elkin Vumar Eccentric connectivity index and eccentric distance sum of some graph operations Transactions on Combinatorics Eccentric connectivity index eccentric distance sum generalized hierarchical product $F$-sum graphs |
| title | Eccentric connectivity index and eccentric distance sum of some graph operations |
| title_full | Eccentric connectivity index and eccentric distance sum of some graph operations |
| title_fullStr | Eccentric connectivity index and eccentric distance sum of some graph operations |
| title_full_unstemmed | Eccentric connectivity index and eccentric distance sum of some graph operations |
| title_short | Eccentric connectivity index and eccentric distance sum of some graph operations |
| title_sort | eccentric connectivity index and eccentric distance sum of some graph operations |
| topic | Eccentric connectivity index eccentric distance sum generalized hierarchical product $F$-sum graphs |
| url | http://www.combinatorics.ir/?_action=showPDF&article=2839&_ob=e28e6997585de2cc61c0727cd04dec50&fileName=full_text.pdf. |
| work_keys_str_mv | AT buzohraguleskender eccentricconnectivityindexandeccentricdistancesumofsomegraphoperations AT elkinvumar eccentricconnectivityindexandeccentricdistancesumofsomegraphoperations |