<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity index, fourth atom-bond connectivity index, sum connectivity index, Randić connectivity index, augmented Zagreb index, Sanskruti index, geometric-arithmetic connectivity index and fifth geometric-arithmetic connectivity index of the line graphs of Banana tree graph and Firecracker graph.</p></abstract>

In this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity index, fourth atom-bond connectivity index, sum connectivity index, Randić connectivity index, augmented Zagreb index, Sanskruti index, geometric-arithmetic connectivity index and fifth geometric-arithmetic connectivity index of the line graphs of Banana tree graph and Firecracker graph.

Computing topological indices of the line graphs of Banana tree graph and Firecracker graph

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity...

(S_u,S_v) : uv ∈ E(G)	(2k + 3,k² − 4k + 7)	(2k + 3,2k + 7)	(2k + 3,k² − 4k + 11)	(2k + 7,k² − 4k + 11)
Number of edges	2	2	2	2
(S_u,S_v) : uv ∈ E(G)	(2k + 7,k² − 4k + 12)	(2k + 7,2k + 8)	(2k + 8,2k + 8)	(k² − 4k + 5,k² − 4k + 7)
Number of edges	2	2	n − 6	2(k − 2)
(S_u,S_v) : uv ∈ E(G)	(k² − 4k + 6,k² − 4k + 7)	(k² − 4k + 11,k² − 4k + 6)	(k² − 4k + 12,k² − 4k + 6)	(k² − 4k + 12,2k + 8)
Number of edges	$\frac{(n - 2) (k^{2} - 5 k + 6)}{2}$ $\begin{array}{} \displaystyle \frac{{(n - 2)({k^2} - 5k + 6)}}{2} \end{array}$	2(k − 2)	(n − 4)(k − 2)	2(n − 5)
(S_u,S_v) : uv ∈ E(G)	(k² − 4k + 5,k² − 4k + 7)
Number of edges	k² − 5k + 6

Computing topological indices of the line graphs of Banana tree graph and Firecracker graph

Published Online: Mar 13, 2017

Page range: 83 - 92

Received: Nov 06, 2016

Accepted: Mar 13, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00007

Keywords
Banana tree graph, Firecracker graph, Topological indices, line graph

© 2017 Muhammad Shoaib Sardar, Sohail Zafar and Zohaib Zahid, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

The size partition of G.

Computing topological indices of the line graphs of Banana tree graph and Firecracker graph

Published Online: Mar 13, 2017

Page range: 83 - 92

Received: Nov 06, 2016

Accepted: Mar 13, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00007

KeywordsBanana tree graph, Firecracker graph, Topological indices, line graph

© 2017 Muhammad Shoaib Sardar, Sohail Zafar and Zohaib Zahid, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

The size partition of G.

Keywords
Banana tree graph, Firecracker graph, Topological indices, line graph