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(β ,α)−Connectivity Index of Graphs

B. Basavanagoud
B. Basavanagoud
, 
Veena R. Desai
Veena R. Desai
 oraz 
Shreekant Patil
Shreekant Patil
   | 30 sty 2017
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Data publikacji: 30 sty 2017
Zakres stron: 21 - 30
Otrzymano: 11 lis 2016
Przyjęty: 30 sty 2017
DOI: https://doi.org/10.21042/AMNS.2017.1.00003
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© 2017 B. Basavanagoud, Veena R. Desai, Shreekant Patil, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Scatter diagram of AcentFacon 2χ1, superimposed by the fitted regression line.
Scatter diagram of AcentFacon 2χ1, superimposed by the fitted regression line.

Fig. 2

(a) 2D-lattice of TUC4C8[4,3]; (b) TUC4C8[4,3] nanotube; (c) TUC4C8[4,3] nanotorus.
(a) 2D-lattice of TUC4C8[4,3]; (b) TUC4C8[4,3] nanotube; (c) TUC4C8[4,3] nanotorus.

Fig. 3

(a) Subdivision graph of 2D-lattice of TUC4C8[4,3]; (b) Line graph of the subdivision graph of 2D-lattice of TUC4C8[4,3].
(a) Subdivision graph of 2D-lattice of TUC4C8[4,3]; (b) Line graph of the subdivision graph of 2D-lattice of TUC4C8[4,3].

Fig. 4

(a) Subdivision graph of TUC4C8[4,3] of nanotube; (b) line graph of the subdivision graph of TUC4C8[4,3] of nanotube.
(a) Subdivision graph of TUC4C8[4,3] of nanotube; (b) line graph of the subdivision graph of TUC4C8[4,3] of nanotube.

Fig. 5

(a) Subdivision graph of TUC4C8[4,3] of nanotorus; (b) Line graph of the subdivision graph of TUC4C8[4,3] of nanotorus.
(a) Subdivision graph of TUC4C8[4,3] of nanotorus; (b) Line graph of the subdivision graph of TUC4C8[4,3] of nanotorus.

Partition of paths of length 2 of the graph Y.

(dY (u), dY(v), dY (w)) where uvw ∈ E2(Y)(2,2,3)(3,3,2)(3,3,3)
Number of paths of length 2 in Y4p8p(36pq — 26p)

Number of vertices and edges.

GraphNumber of verticesNumber of edges
2D-lattice of TUC4C8 [p,q]4pq6pq − p − q
TUC4C8[p,q] nanotube4pq6 pq — p
TUC4C8[p,q] nanotorus4pq6pq

Partition of paths of length 2 of the graph X.

(dx(u), dX (v), dX (w)) where uvw ∈ E2(X)(2,2,2)(2,2,3)(3,3,2)(3,3,3)
Number of paths of length 2 in X84(p + q — 2)8(p + q — 2)(36 pq — 26 p — 26q + 16)

Partition of paths of length 2 of the graph A = L(S(Tn,k)) for k = 1

(dA(u), dA(v), dA (w)) where uvw ∈ E2(A)(1,3,3)(2,3,3)(2,2,3)(3,3,3)(2,2,2)
Number of paths of length 2 in A24232n − 4

Partition of paths of length 2 of the graph A = L(S(Tn,k)) for k > 1

(dA(u), dA(v), dA(w)) where uvw ∈ E2(A)(1,2,2)(2,3,3)(2,2,3)(3,3,3)(2,2,2)
Number of paths of length 2 in A16332n + 2k – 8

Partition of paths of length 2 of the graph C.

(dC(u),dC(v),dC(w))where uvwe E2(C)(2,2,2)(2,2,3)(2,3,3)(3,3,3)
Number of paths of length 2 in C44818n — 44

Partition of paths of length 2 of the graph B.

(dB(u),dB(v),dB(w)) where uvw e E2(B)(3,3,3)(3,3,n)(3,n,n)(n,n,n)
Number of paths of length 2 in B7n2nn(n —1)n(n−1)(n−2)2$\frac{{n\left( {n - 1} \right)\left( {n - 2} \right)}}{2}$

Experimental values of the acentric factor and corresponding values of 2χ1 of octane isomers.

AlkaneAcentFac2χ1
n-octane0.39789840
2-methyl-heptane0.37791647
3-methyl-heptane0.37100254
4-methyl-heptane0.37150456
3-ethyl-hexane0.36247264
2,2-dimethyl-hexane0.33942664
2,3-dimethyl-hexane0.34824770
2,4-dimethyl-hexane0.34422363
2,5-dimethyl-hexane0.3568354
3,3-dimethyl-hexane0.32259680
3,4-dimethyl-hexane0.34034578
2-methyl-3-ethyl-pentane0.33243381
3-methyl-3-ethyl-pentane0.30689996
2,2,3-trimethyl-pentane0.30081696
2,2,4-trimethyl-pentane0.3053775
2,3,3-trimethyl-pentane0.293177103
2,3,4-trimethyl-pentane0.31742287
2,2,3,3-tetramethylbutane0.255294120
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