**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32918

##### Metric Dimension on Line Graph of Honeycomb Networks

**Authors:**
M. Hussain,
Aqsa Farooq

**Abstract:**

**Keywords:**
Resolving set,
metric dimension,
honeycomb network,
line graph.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.3593128

**References:**

[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England: Addison-Wesley, 1999.

[2] E.T. Baskoro, A.N.M. Salman, S.W. Saputro, D. Suprijanto, On metric dimension of regular bipartite graphs, Bull.Math.Soc.Sci.Math.Roumanie, 54(102), 1, 15 − 28, (2011).

[3] P. S. Buczkowski, G. Chartrand, C. Poisson, P. Zhang, On k-dimensional graphs and their bases, Perioddica Math. HUNG 46(1)(2003)9 − 15.

[4] J.C. Bermound, F. Comellas, D.F. Hsu, Distributed loop computer networks, survey, J. Parallel Distrib. Comput. 24(1995)2-10.

[5] P.J. Cameron, J.H. Van Lint, Designs, Graphs, Codes and Their Links, in London Mathematical society student Texts, vol.22, Cambridge University Press, Cambridge,1991.

[6] T.Y. Feng, A Survey of interconnection Networks, IEEE Comput., pages 12 − 27, 1981.

[7] F. Harary, R.A. Melter, On the metric dimension of a graph, Ars Combin.2(1976)191 − 195.

[8] W.D. Hills, The connection Machine, IEEE Comput., pages 12−27, 1981.

[9] K. Hwang and J. Ghosh, Hypernet, A Communication-Efficient, Architecture for constructing Massvely parallel computers, IEEE Trans. on Comput., vol. C-36,Pages,1450 − 1466, 1987.

[10] M. Imran, A.Q. Baig, S.A.U.H. Bokhary, I. Javaid On the metric dimension Applied Mathematics Letters, 25(2012)320 − 325.

[11] S. Khuller, B. Raghavachari, A. Rosenfeld, Localization in graphs, Technical report CS-TR-3326, University of Maryland at College Park, 1994.

[12] P. Manuel, B. Rajan, I. Rajasingh, C. Monica, On minimum metric dimension of honeycom networks Journal of Discrete Algorithms, 6(2008)20 − 27.

[13] R.A. Melter, I. Tomescu, Metric bases in digital geometry Journal of Discrete Algorithms, 6(2008)20 − 27.

[14] A. Seb¨o, E. Tannier, On metric generators of graphs Math.Oper. Res. 29(2004)383 − .

[15] P.J. Slater, Dominating and references sets in graphs J. Math.Phys.sci 22(1988)445 − .

[16] P.J. Slater, Leaves of trees Congress. Number. 14(1975)549 − 559.

[17] I. Tomescu, M. Imran, Metric Dimension and R-Sets of Connected Graph Graphs and Combinatorics, 27(2011), 585 − 591.

[18] R.S. Wilkov, Analysis and Design of Reliable computer Networks IEEE Trans.on commun, vol. COM-20, pages 660 − 678, 1972.

[19] Simonraj F., George A., on the metric Dimension of silicate stars ARPN Journal of Engineering and Applied Sciences 2015; 05 : 2187 − 2192.

[20] Simonraj F., George A., Embedding of poly honeycomb networks and the metric dimension of star of david network International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC).2012; 04 : 11 − 28.

[21] S. P. Eu, T. S. Fu, A simple proof of the aztec diamond theorem The Electronic Journal of Combinatorics, (2005).12.

[22] Godsil C., McKay B. A new graph product and its spectrum Bulletin of the Australian Mathematical Society. 1978; 18 : 21 − 8.