<abstract xmlns="http://www.w3.org/1999/xhtml">

Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausi-2023-0009_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><munder><mo>∑</mo><mrow><mi>ν</mi><mo>∈</mo><mtext>V</mtext><mrow><mo>(</mo><mtext>G</mtext><mo>)</mo></mrow></mrow></munder><mrow><mtext>ec</mtext><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow><mtext> </mtext><mtext>deg</mtext><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></mrow></math>
<tex-math>\sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)}</tex-math>
</alternatives>
</inline-formula> where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.
</abstract>

Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as 


∑ν∈V(G)ec(ν) deg(ν)
\sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)}

 where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.

Eccentric connectivity index in transformation graph Gxy+

Faculty of Sciences, Department of Mathematics

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Eccentric connectivity index in transformation graph G

{"article-title":{"content":"Eccentric connectivity index in transformation graph G","sup":"xy+"}}

Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as...

Eccentric connectivity index in transformation graph G^xy+

Published Online: Aug 08, 2023

Page range: 111 - 123

Received: Jan 18, 2023

DOI: https://doi.org/10.2478/ausi-2023-0009

Keywords
Distance, eccentricity, eccentric connectivity index, transformation graph

© 2023 Aysun Aytaç et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Eccentric connectivity index in transformation graph Gxy+

Published Online: Aug 08, 2023

Page range: 111 - 123

Received: Jan 18, 2023

DOI: https://doi.org/10.2478/ausi-2023-0009

KeywordsDistance, eccentricity, eccentric connectivity index, transformation graph

© 2023 Aysun Aytaç et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Eccentric connectivity index in transformation graph G^xy+

Keywords
Distance, eccentricity, eccentric connectivity index, transformation graph