Search Results

1 - 6 of 6 items :

  • L(2, 1)-Labeling of Circulant Graphs x
Clear All
L(2, 1)-Labeling of Circulant Graphs

References [1] T. Araki, Labeling bipartite permutation graphs with a condition at distance two, Discrete Appl. Math. 157 (2009) 1677-1686. doi: 10.1016/j.dam.2009.02.004 [2] P. Bahls, Channel assignment on Cayley graphs, J. Graph Theory 67 (2011) 169-177. doi: 10.1002/jgt.20523 [3] H.L. Bodlaender, T. Kloks, R.B. Tan and J. van Leeuwen, Approximations for λ- colorings of graphs, Comput. J. 47 (2004) 193-204. doi: 10.1093/comjnl/47.2.193 [4] J.A. Bondy and U.S.R.Murty, Graph Theory (Springer, New

Open access
Supermagic Generalized Double Graphs

1 This work was supported by the Slovak VEGA Grant 1/0652/12. References [1] L’. Bezegová and J. Ivančo, An extension of regular supermagic graphs , Discrete Math. 310 (2010) 3571–3578. doi:10.1016/j.disc.2010.09.005 [2] L’. Bezegová and J. Ivančo, On conservative and supermagic graphs , Discrete Math. 311 (2011) 2428–2436. doi:10.1016/j.disc.2011.07.014 [3] R. Bodendiek and G. Walther, Arithmetisch antimagische graphen , in: Graphentheorie III, K. Wagner, R. Bodendiek (Ed(s)), (BI-Wiss. Verl., Mannheim, 1993). [4] R

Open access
On the uniqueness of d-vertex magic constant

References [1] S. Arumugam, D. Fronček and N. Kamatchi, Distance magic graphs-A survey, J. Indones. Math. Soc., Special Edition (2011) 11-26. [2] S. Beena, On ∑ and ∑′ labelled graphs, Discrete Math. 309 (2009) 1783-1787. doi:10.1016/j.disc.2008.02.038 [3] G. Chartrand and L. Lesniak, Graphs & Digraphs, 4th Edition (Chapman and Hall, CRC, 2005). [4] D. Grinstead and P.J. Slater, Fractional domination and fractional packings in graphs, Congr. Numer. 71 (1990) 153-172. [5] T

Open access
Constant Sum Partition of Sets of Integers and Distance Magic Graphs

R eferences [1] Y. Alavi, A.J. Boals, G. Chartrand, P. Erdős and O.R. Oellerman, The ascending subgraph decomposition problem , Congr. Numer. 58 (1987) 7–14. [2] K. Ando, S. Gervacio and M. Kano, Disjoint subsets of integers having a constant sum , Discrete Math. 82 (1990) 7–11. doi:10.1016/0012-365X(90)90040-O [3] M. Anholcer and S. Cichacz, Note on distance magic products G ◦ C 4 , Graphs Combin. 31 (2015) 1117–1124. doi:10.1007/s00373-014-1453-x [4] M. Anholcer, S. Cichacz, I. Peterin and A. Tepeh, Distance magic labeling

Open access
The Spectrum Problem for the Connected Cubic Graphs of Order 10

References [1] P. Adams and D. Bryant, The spectrum problem for the Petersen graph , J. Graph Theory 22 (1996) 175–180. doi:10.1002/(SICI)1097-0118(199606)22:2〈175::AID-JGT8〉3.0.CO;2-K [2] P. Adams, D. Bryant and M. Buchanan, A survey on the existence of G-designs , J. Combin. Des. 16 (2008) 373–410. doi:10.1002/jcd.20170 [3] P. Adams, D. Bryant and A. Khodkar, Uniform 3 -factorisations of K 10 , Congr. Numer. 127 (1997) 23–32. [4] P. Adams, C. Chan, S.I. El-Zanati, E. Holdaway, U. Odabaşı and J. Ward, The spectrum problem for

Open access
On graphs with equal dominating and c-dominating energy

) := det ( μI – A D ( G )). The minimum dominating eigenvalues of a graph G are the eigenvalues of A D ( G ). Since A D ( G ) is real and symmetric, its eigenvalues are real numbers and we label them in non-increasing order μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n . The minimum dominating energy of G is then defined as E D ( G ) = ∑ i = 1 n | μ i | . $$\begin{array}{} \displaystyle E_{D}(G) = \sum \limits _{i=1}^n |\mu_i|. \end{array}$$ Motivated by dominating matrix, here we define the minimum connected dominating matrix abbreviated as (c-dominating matrix). The c

Open access