The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census

Rika Yanti, Gregory Benedict Tanidi, Suhadi Wido Saputro, Edy Tri Baskoro


Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.


symmetric cubic graphs, total vertex irregularity strength, algorithms, Foster's census

Full Text:




M. Bača, S. Jendrol', M. Miller, J. Ryan, On Irregular Total Labellings, Discrete Math., 307 (2005), 1378--1388.

I. Z. Bouwer, W.W. Chernoff, B. Monson, and Z. Star, The Foster Census, Charles Babbage Research Centre, (1988).

G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz, F. Saba, Irregular Networks, Congr. Numer., 64 (1988), 187--192.

M. Conder, P. Dobcsányi, Trivalent Symmetric Graphs Up to 768 Vertices, J. Combin. Math. Combin. Comput., 40 (2002), 41-63.

M. Conder, Trivalent (cubic) Symmetric Graphs on Up to 2048 Vertices,

D. A. Holton, J. Sheehan, The Petersen graph, Cambridge University Press, (1993).

Nurdin, E.T. Baskoro, N.N. Gaos, A.N.M. Salman, On the Total Vertex Irregularity Strength of Trees, Discrete Math., 310 (2010), 3043--3048.

Rikayanti and E.T. Baskoro, Algorithms of Computing the Total Vertex Irregularity Strength of Some Cubic Graphs, Int. J. Math. Comput. Sci., 16(3) (2021), 897-905.

S. Jendrol, V. Zoldak, The Irregularity Strength of Generalized Petersen Graphs, Math. Slovaca, 45 (1995), 107--113.

D.R. Silaban, E.T. Baskoro, H. Kekaleniate, S. Lutpiah, K.A. Sugeng, Algorithm to Construct Graph with Total Vertex Irregularity Strength Two, Procedia Comput. Sci., 74 (2015), 132--137.

R. Ramdani, A.N.M. Salman, H. Assiyatun, On the Total Irregularity Strength of Regular Graphs, J. Math. Fund. Sci., 47 (2015), 281--295.

Susilawati, E.T. Baskoro, R. Simanjuntak, Total Vertex-irregularity Labelings for Subdivision of Several Classes of Trees, Procedia Comput. Sci., 74 (2015), 112--117.

Susilawati, E.T. Baskoro, R. Simanjuntak, Total vertex irregularity strength of trees with maximum degree five, Electron. J. Graph Theory Appl., 6 (2) (2018), 250--257.

Royle. G, Cubic Symmetric Graphs (The Foster Census),


  • There are currently no refbacks.

ISSN: 2541-2205

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View IJC Stats