Main Article Content
Abstract
Cellulose is one of the natural bio-polymers which have been extensively used in various
fields due to their valuable and remarkable chemical and physical properties. Due to a key ingredients
of cellulose in various product, it’s applications have widely been recognized in many industries like
pharmaceutical, bio-fuel, textiles, etc. The study of graphs using chemistry attracts a lot of researchers
globally because of its enormous application. One such application is studying topological indices is a
numerical value of a chemical graph associated to a molecular structure. This work attempts to compute
cellulose chemical structure using topological indices based on the bond like szeged, Padmakar-Ivan(PI),
weighted version of PI and szeged index and its polynomial.
Keywords
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
- Arockiaraj, M., Mushtaq, S., Klavˇzar, S., Celin Fiona, J., Balasubramanian, K., Szeged-like
- topological indices and the efficacy of the cut method: The case of melem structures, Discrete
- Math. Lett. 9, (2022), 49-56.
- Ali, P., Ajaz, P., Kirmani, K., Rugaie, O.A., and AzamKwong, F., Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates, Saudi Pharmaceutical
- Journal, 28, (2020), 1093-1100.
- Asif, M. and Hussain, M., Topological characterization of cellulose network Comp. J. Combin.
- Math., 2, (2020), 21-30.
- Ali, A., and Dosli ˇ c´, T., Mostar index: Result and perspectives, Appl.Math.Comput.
- ,(2021), Article ID: 126245.
- Alhevaz, A., Baghipur, M. and Shang, Y., On Generalized Distance Gaussian Estrada Index
- of Graphs Symmetry, 11(10), 1276, 2019.
- Arokiaraj, M., Clement, J., Tratnik, N., Mushtaq, S., and Balasubramanian, K.,Weighted
- Mostar indices as Mostar indices as measures of molecular peripheral shapes with application
- to graphene, graphdiyne and graphdiyne nanoribbons, SAR QSAR Environ.Res., 31, (2020),
- -208.
- Ashrafi, A.R., Ghorbani, M., and Jalali, M., The PI and Edge Szeged Polynomials of an
- Infinite Family of Fullerenes, Nanotubes and Carbon Nanostructures, 18(2), (2010), 1536-
- Ahmad, M., Saeed, M., Javaid, M., and Bonyah, E., Molecular Descriptor Analysis of Certain
- Isomeric Natural Polymers, Hindawi Journal of Chemistry, 26, (2021), Article ID 9283246.
- Brezovnik, S. and Tratnik, N., General cut method for computing szeged-like topological
- indices with application to molecular graphs, International Journal of Quantum Chemistry,
- (2), (2021), Article ID: e26530.
- Cash, G.G., Relationship Between the Hosoya Polynomial and the Hyper-Wiener Index,
- Applied Mathematics Letters, 15, (2002), 893-895.
- Cruz-Medina, R., Ayala-Hern´andez, D.A. et al, Curing of Cellulose Hydro gels by UV Radiation for Mechanical Reinforcement, MDIP, 13, (2021), 23-42.
- Dobrynin, A., The Szeged and Wiener indices of line graphs,MATCH Commun. Math. Comput. Chem., 79, (2018), 743-756.
- Dosli ˇ c´, T. and Martinjak, I., Sˇkrekovski, R., Spuzevi ˇ c´, S.T. and Zubac, I., Mostar index,
- Journal of mathematical chemistry, 56(10), (2018), 2995-3013.
- Ghorbani, M. and Jalali, M., The Vertex PI, Szeged and Omega Polynomials of Carbon
- Nanocones CNC4[n], MATCH Commun. Math. Comput. Chem. 62, (2009), 353-362.
- Ghorbani, M. and Hemmasi, M., The Vertex PI and Szeged Polynomials of an Infinite Family
- of Fullerenes, Journal of Computational and Theoretical Nanoscience, 7, (2010), 2411-2415.
- Gutman, I. and Dobrynin, A., The Szeged index - a success story,Graph Theory Notes New
- York, 34, (1998), 37-44.
- Gutman, I. and Ashrafi, A.R., On the PI Index of Phenylenes and their Hexagonal Squeezes,
- MATCH Commun. Math. Comput. Chem., 60, (2008), 135-142.
- Gupta, P.K., Raghunath, S.S., Prasanna, D.V., Venkat, P., Shree, D.V., Chithananthan,
- C., Choudhary, S., Surender, K., and Geetha, K., An Update on Overview of Cellulose, Its
- Structure and Applications, web of science, intech open, (2019), 1-23
- Ilic´, A. and M ilosavljevic´, N., The weighted vertex PI index, Mathematical and Modeling,
- ,(2013), 627-631.
- Kirmani, S.A.K., Ali, P. and Azam, F., Topological indices and QSPR/QSAR analysis of
- some antiviral-drugs being investigated for the treatment of COVID-19 patients, Int J Quantum Chem., 121, (2021), Article ID: e26594.
- Khalaf, A.J.M., et al, Degree-based topological indices and polynomial of cellulose, Journal
- of prime in mathematics, 17(1), (2021), 70-78.
- Kandan, P. and Subramanian, S., On Mostar index of graph, Advances in Mathematics:
- Scientific Journal, 10(4), (2021), 2115-2129.
- Kandan, P., Subramanian, S., and Rajesh, P., Weighted Mostar indices of certain graphs,
- Advance in mathematics:Scientific journal, 10(9), (2021), 3093-3111.
- Kandan, P. and Subramanian, S., Computation of Weighted PI and Szeged Indices of Conical
- Graph, Indian Journal of Natural Sciences, 12(69), 2021, 36933-36941.
- Kandan, P. and Subramanian, S., Mostar index of Conical and Generalized gear graph Commun. Combin., Cryptogr. and Computer Sci., 2, (2022), 1-9.
- Kandan, P. and Subramanian, S., Some bound-additive indices of graohs (ICDM2021-MSU)
- -93-91077-53-2, 1-7, (confrence procceding).
- Kandan, P. and Subramanian, S., Weighted PI and Szeged indices of generlized gear graph,
- Indian Journal of Natural Sciences, 13(72), (2022), 41816-41823.
- Kandan, P., Subramanian, S., and Rajesh, P., Calculating PI related indices and their polynomial of Hyaluronic Acid and Conjugates, J. Indones. Math. Soc., 28(2), (2022), 194-214.
- Kumar, R., Sharma, R.K., and Singh, A.P., Grafted cellulose: A bio-based polymer for durable
- applications, Polym. Bull., 75, (2018), 2213-2242.
- Khadikar, P.V., Karmarkar, S., Agrawal, V.K., Singh, J., Shrivastava, J., Lukovits, I., and
- Diudea, M.V., Szeged index Applications for drug modeling, Lett. Drug Design Disc., 2,
- (2005), 606-624.
- Khadikar, P.V. and Karmarkar, S., A novel PI index and its applications to QSPR/QSAR
- studies, J. Chem. Inf. Comput. Sci., 41, (2001), 934-949.
- Khalifeh, M.H., Yousefi, H., and Ashrafi, A.R., Vertex and edge PI-indices of Cartesian
- Product graphs, Discrete Appl. Math., 156, (2008), 1780-1789.
- Mirzargar, M., PI, Szeged and Edge Szeged Polynomials of a Dendrimer Nanostar, MATCH
- Commun. Math. Comput. Chem., 62, (2009), 363-370.
- Makowsky, J.A., Ravve, E.V., and Blanchard, N.K., On the location of roots of graph polynomials, European Journal of Combinatorics, 41, (2014), 1-19.
- Pattabiraman, K. and Kandan, P., Weighted szeged index of graphs, Bulletin of the International mathematical virtual institute, 8, (2018), 11-19.
- Pattabiraman, K. and Kandan, P., On weighted PI index of graphs, Electronic notes in
- discrete mathematics, 53, (2016), 225-238.
- Shang, Y., A remark on the chromatic polynomial of in comparability graphs of posets, PLoS
- ONE, 10(3), (2014), 17-31.
- Shang, Y., Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs
- Mathematics, 2020, 8, 1063.
- Shang, Y., Sombor index and degree-related properties of simplicial networksApplied Mathematics and Computation, 419. p. 126881. ISSN 0096-3003.
- Tranik, N., Computing weighted Szeged and PI indices from quotient graphs, Int J Quantum
- Chem., (2019), Article ID: e26006.
- Trinajstic, N., Chemical Graph Theory, CRC Press, Boca Raton, FL, USA, Volum I/II, 1983.
- Tang, Z., Wu, Z., Cheu, H., and Deng, H., This distance spectrum ot two new operations of
- graphs,Transactions on Combinatorics, 9(3), (2020), 125-138.
- Wang, J., Wang, Y., Wang, Y., and Zheng, L., Computational on the topological indices of
- hyaluronic acid,Journal of Applied Analysis and Computation, 3(10), (2020), 1193-1198.
- Wang, Z., Mao, Y., Das, K.C., and Shang, Y., Nordhaus–Gaddum-Type Results for the
- Steiner Gutman Index of Graphs Symmetry, 12, 2020, 1711
References
Arockiaraj, M., Mushtaq, S., Klavˇzar, S., Celin Fiona, J., Balasubramanian, K., Szeged-like
topological indices and the efficacy of the cut method: The case of melem structures, Discrete
Math. Lett. 9, (2022), 49-56.
Ali, P., Ajaz, P., Kirmani, K., Rugaie, O.A., and AzamKwong, F., Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates, Saudi Pharmaceutical
Journal, 28, (2020), 1093-1100.
Asif, M. and Hussain, M., Topological characterization of cellulose network Comp. J. Combin.
Math., 2, (2020), 21-30.
Ali, A., and Dosli ˇ c´, T., Mostar index: Result and perspectives, Appl.Math.Comput.
,(2021), Article ID: 126245.
Alhevaz, A., Baghipur, M. and Shang, Y., On Generalized Distance Gaussian Estrada Index
of Graphs Symmetry, 11(10), 1276, 2019.
Arokiaraj, M., Clement, J., Tratnik, N., Mushtaq, S., and Balasubramanian, K.,Weighted
Mostar indices as Mostar indices as measures of molecular peripheral shapes with application
to graphene, graphdiyne and graphdiyne nanoribbons, SAR QSAR Environ.Res., 31, (2020),
-208.
Ashrafi, A.R., Ghorbani, M., and Jalali, M., The PI and Edge Szeged Polynomials of an
Infinite Family of Fullerenes, Nanotubes and Carbon Nanostructures, 18(2), (2010), 1536-
Ahmad, M., Saeed, M., Javaid, M., and Bonyah, E., Molecular Descriptor Analysis of Certain
Isomeric Natural Polymers, Hindawi Journal of Chemistry, 26, (2021), Article ID 9283246.
Brezovnik, S. and Tratnik, N., General cut method for computing szeged-like topological
indices with application to molecular graphs, International Journal of Quantum Chemistry,
(2), (2021), Article ID: e26530.
Cash, G.G., Relationship Between the Hosoya Polynomial and the Hyper-Wiener Index,
Applied Mathematics Letters, 15, (2002), 893-895.
Cruz-Medina, R., Ayala-Hern´andez, D.A. et al, Curing of Cellulose Hydro gels by UV Radiation for Mechanical Reinforcement, MDIP, 13, (2021), 23-42.
Dobrynin, A., The Szeged and Wiener indices of line graphs,MATCH Commun. Math. Comput. Chem., 79, (2018), 743-756.
Dosli ˇ c´, T. and Martinjak, I., Sˇkrekovski, R., Spuzevi ˇ c´, S.T. and Zubac, I., Mostar index,
Journal of mathematical chemistry, 56(10), (2018), 2995-3013.
Ghorbani, M. and Jalali, M., The Vertex PI, Szeged and Omega Polynomials of Carbon
Nanocones CNC4[n], MATCH Commun. Math. Comput. Chem. 62, (2009), 353-362.
Ghorbani, M. and Hemmasi, M., The Vertex PI and Szeged Polynomials of an Infinite Family
of Fullerenes, Journal of Computational and Theoretical Nanoscience, 7, (2010), 2411-2415.
Gutman, I. and Dobrynin, A., The Szeged index - a success story,Graph Theory Notes New
York, 34, (1998), 37-44.
Gutman, I. and Ashrafi, A.R., On the PI Index of Phenylenes and their Hexagonal Squeezes,
MATCH Commun. Math. Comput. Chem., 60, (2008), 135-142.
Gupta, P.K., Raghunath, S.S., Prasanna, D.V., Venkat, P., Shree, D.V., Chithananthan,
C., Choudhary, S., Surender, K., and Geetha, K., An Update on Overview of Cellulose, Its
Structure and Applications, web of science, intech open, (2019), 1-23
Ilic´, A. and M ilosavljevic´, N., The weighted vertex PI index, Mathematical and Modeling,
,(2013), 627-631.
Kirmani, S.A.K., Ali, P. and Azam, F., Topological indices and QSPR/QSAR analysis of
some antiviral-drugs being investigated for the treatment of COVID-19 patients, Int J Quantum Chem., 121, (2021), Article ID: e26594.
Khalaf, A.J.M., et al, Degree-based topological indices and polynomial of cellulose, Journal
of prime in mathematics, 17(1), (2021), 70-78.
Kandan, P. and Subramanian, S., On Mostar index of graph, Advances in Mathematics:
Scientific Journal, 10(4), (2021), 2115-2129.
Kandan, P., Subramanian, S., and Rajesh, P., Weighted Mostar indices of certain graphs,
Advance in mathematics:Scientific journal, 10(9), (2021), 3093-3111.
Kandan, P. and Subramanian, S., Computation of Weighted PI and Szeged Indices of Conical
Graph, Indian Journal of Natural Sciences, 12(69), 2021, 36933-36941.
Kandan, P. and Subramanian, S., Mostar index of Conical and Generalized gear graph Commun. Combin., Cryptogr. and Computer Sci., 2, (2022), 1-9.
Kandan, P. and Subramanian, S., Some bound-additive indices of graohs (ICDM2021-MSU)
-93-91077-53-2, 1-7, (confrence procceding).
Kandan, P. and Subramanian, S., Weighted PI and Szeged indices of generlized gear graph,
Indian Journal of Natural Sciences, 13(72), (2022), 41816-41823.
Kandan, P., Subramanian, S., and Rajesh, P., Calculating PI related indices and their polynomial of Hyaluronic Acid and Conjugates, J. Indones. Math. Soc., 28(2), (2022), 194-214.
Kumar, R., Sharma, R.K., and Singh, A.P., Grafted cellulose: A bio-based polymer for durable
applications, Polym. Bull., 75, (2018), 2213-2242.
Khadikar, P.V., Karmarkar, S., Agrawal, V.K., Singh, J., Shrivastava, J., Lukovits, I., and
Diudea, M.V., Szeged index Applications for drug modeling, Lett. Drug Design Disc., 2,
(2005), 606-624.
Khadikar, P.V. and Karmarkar, S., A novel PI index and its applications to QSPR/QSAR
studies, J. Chem. Inf. Comput. Sci., 41, (2001), 934-949.
Khalifeh, M.H., Yousefi, H., and Ashrafi, A.R., Vertex and edge PI-indices of Cartesian
Product graphs, Discrete Appl. Math., 156, (2008), 1780-1789.
Mirzargar, M., PI, Szeged and Edge Szeged Polynomials of a Dendrimer Nanostar, MATCH
Commun. Math. Comput. Chem., 62, (2009), 363-370.
Makowsky, J.A., Ravve, E.V., and Blanchard, N.K., On the location of roots of graph polynomials, European Journal of Combinatorics, 41, (2014), 1-19.
Pattabiraman, K. and Kandan, P., Weighted szeged index of graphs, Bulletin of the International mathematical virtual institute, 8, (2018), 11-19.
Pattabiraman, K. and Kandan, P., On weighted PI index of graphs, Electronic notes in
discrete mathematics, 53, (2016), 225-238.
Shang, Y., A remark on the chromatic polynomial of in comparability graphs of posets, PLoS
ONE, 10(3), (2014), 17-31.
Shang, Y., Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs
Mathematics, 2020, 8, 1063.
Shang, Y., Sombor index and degree-related properties of simplicial networksApplied Mathematics and Computation, 419. p. 126881. ISSN 0096-3003.
Tranik, N., Computing weighted Szeged and PI indices from quotient graphs, Int J Quantum
Chem., (2019), Article ID: e26006.
Trinajstic, N., Chemical Graph Theory, CRC Press, Boca Raton, FL, USA, Volum I/II, 1983.
Tang, Z., Wu, Z., Cheu, H., and Deng, H., This distance spectrum ot two new operations of
graphs,Transactions on Combinatorics, 9(3), (2020), 125-138.
Wang, J., Wang, Y., Wang, Y., and Zheng, L., Computational on the topological indices of
hyaluronic acid,Journal of Applied Analysis and Computation, 3(10), (2020), 1193-1198.
Wang, Z., Mao, Y., Das, K.C., and Shang, Y., Nordhaus–Gaddum-Type Results for the
Steiner Gutman Index of Graphs Symmetry, 12, 2020, 1711