Upper Bound Sequences of Rotationally Symmetric Triangular Prism Constructed as Halin Graph Using Local Fractional Metric Dimension

Mamoona Farooq, Asif Abd ul Rehman, M. Khalid Mahmood, Daud Ahmad


In this paper, we consider rotationally symmetric traingular planar network with possible planar symmetries. We find local fractional metric dimension of planar symmetries. The objective is to search sequences of local fractional metric dimension of triangular prism planar networks by joining different copies. We propose and prove generalized formulas of all sequences for local fractinal metric
dimension over triangular prism.

Full Text:



Carmen Hernando, Merce Mora,Ignacio M.Pelayo,carlos Seara on the metric dimension of some families of graphs

(2005):129 133.

shahbaz ali, Muhammad khalid, Mahmood Fairouz Tchier and F.M.O Tawfiq on the classification of upper bound sequences

of local fractional metric dimension of rotationally symmetric hexagonal planar networks. 2(2021):29 37.

P. J. Slater, Leaves of trees, Congressus Numerantium, vol. 14, pp. 549559, 1975

P. J. Slater, Dominating and reference sets in a graph, Journal of Mathematical and Physical Sciences, vol. 22, no. 4, pp.

, 1988

P. J. Slater, Domination and location in acyclic graphs, Networks, vol. 17, no. 1, pp. 5564, 1987.

M. Imran, A. Q. Baig, M. K. Sha?q, and I. Tomescu, On metric dimension of generalized Petersen graphs P(n;3), ARS

Combinatoria, vol. 117, pp. 113130, 2014.

J.-B.Liu,C.Wang,S.Wang,andB.Wei,Zagrebindicesand multiplicative zagreb indices of eulerian graphs, Bulletin of the

Malaysian Mathematical Sciences Society, vol. 42, no. 1, pp. 6778, 2019.

J.-B. Liu and S. N. Daoud, Number of spanning trees in the sequence of some graphs, Complexity, vol. 2019, Article ID

, 22 pages, 2019

J.-B. Liu, X.-F. Pan, and J. Cao, Some properties on Estrada index of folded hypercubes networks, Abstract and Applied

Analysis, vol. 2014, Article ID 167623, 6 pages, 2014.

J. B. Liu, Z. Y. Shi, Y. H. Pan, J. Cao, M. Abdel-Aty, and U. Al-Juboori, Computing the laplacian spectrum of linear

octagonal-quadrilateral networks and its applications, Polycyclic Aromatic Compounds, pp. 1-2, 2020.

G.Chartrand,L.Eroh,M.A.Johnson,andO.R.Oellermann, Resolvabilityingraphsandthemetricdimensionofagraph, Discrete

Applied Mathematics, vol. 105, no. 13, pp. 99113, 2000.

J. Currie and O. R. Oellermann, The metric dimension and metric independence of a graph, Journal of Combinatorial

Mathematics and Combinatorial Computing, vol. 39, pp. 157167, 2001.

Ali, S., Mahmood K., (2019), New numbers on Euler’s totient function with apllications, Journal of Mathematical extension

, 61-83.

Mahmood, M. K., Ali, S., (2019), On Super Totient Numbers, With Applications And Algorithms To Graph Labeling. Ars

Combinatoria, 143, 29-37.

Mahmood, M. K., Ali, S., (2017), A novel labeling algorithm on several classes of graphs, Punjab Univ. j. math, 49, 23-35.

Ali, S., Mahmood, M. K., Mateen, M. H., (2019), New Labeling Algorithm on Various Classes of Graphs with Applications,

In 2019 International Conference on Innovative Computing (ICIC) (pp. 1-6), IEEE.

Ali, S., Mahmood, M. K., (2021), A paradigmatic approach to investigate restricted totient graphs and their indices,

Computer Science, 16(2), 793-801.

Ali, S., Mahmmod, M. K., Falcn, R. M., (2021), A paradigmatic approach to investigate restricted hyper totient graphs,

AIMS Mathematics, 6(4), 3761-3771.

Mateen, M. Haris, M. Khalid Mahmood, Daud Ahmad, Shahbaz Ali, and Shajib Ali. ”A Paradigmatic Approach to Find

Equal Sum Partitions of Zero-Divisors via Complete Graphs.” Journal of Chemistry 2022 (2022).

Mateen, M. Haris, M. Khalid Mahmood, Shahbaz Ali, and M. D. Alam. ”On Symmetry of Complete Graphs over Quadratic

and Cubic Residues.” Journal of Chemistry 2021 (2021).

Mateen, M. Haris, Muhammad Khalid Mahmmod, Doha A. Kattan, and Shahbaz Ali. ”A novel approach to find partitions

of Z

with equal sum subsets via complete graphs.” AIMS Mathematics 6, no. 9 (2021): 9998-10024.

Ali, Shahbaz, Ral M. Falcn, and Muhammad Khalid Mahmood. ”Local fractional metric dimension of rotationally sym-


metric planar graphs arisen from planar chorded cycles.” arXiv preprint arXiv:2105.07808 (2021).

Ali, Shahbaz, Muhammad Khalid Mahmood, and Kar Ping Shum. ”Novel classes of integers and their applications in

graph labeling.” Hacettepe J. Math. Stat 1 (2021): 1-17.

Mahmood, M. Khalid, and Lubna Anwar. ”Loops in Digraphs of Lambert Mapping Modulo Prime Powers: Enumerations

and Applications.” Advances in Pure Mathematics 6, no. 08 (2016): 564.

M. Aslam Malik and M. Khalid Mahmood, On Simple Graphs Arising From Exponential Congruences, Journal of Applied

Mathematics, Volume 2012, Article ID 292895, 10 pages. doi:10.1155/2012/292895.

M. Khalid Mahmood and Farooq Ahmad, A Classication of Cyclic Nodes and Enumerations of Components of a Class

of Discrete Graphs, 9(1) (2015), PP: 103-112. Doi:10.12785/amis/090115.

DOI: http://dx.doi.org/10.21015/vtm.v9i1.1020


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.