Yıl 2018, Cilt 47, Sayı 3, Sayfalar 513 - 519 2018-06-01

On super edge-magic deficiency of certain Toeplitz graphs

Ali Ahmad [1] , Muhammad Faisal Nadeem [2] , Ashok Gupta [3]

40 30

A graph $G$ is called edge-magic if there exists a bijective function $\phi:V(G)\cup E(G)\to\{1, 2,\dots,|V(G)|+|E(G)|\}$ such that $\phi(x)+\phi(xy)+\phi(y)=c(\phi)$ is a constant for every edge $xy\in E(G)$, called the valence of $\phi$. Moreover, $G$ is said to be super edge-magic if $\phi(V(G))=\{1,2,\dots,|V(G)|\}.$ The super edge-magic deficiency of a graph $G$, denoted by $\mu_s(G)$, is the minimum nonnegative integer $n$ such that $G\cup nK_1,$ has a super edge-magic labeling, if such integer does not exist we define $\mu_s(G)$ to be $+\infty.$ In this paper, we study the super edge-magic deficiency of some Toeplitz graphs.

edge-magic, super edge-magic, Toeplitz graphs
  • B. D. Acharya, S. M. Hegde, Strongly indexable graphs, Discrete Math., 93 (1991), 123129.
  • A. Ahmad, I. Javaid , M. F. Nadeem and R. Hasni, On Super edge-magic deciency of some families related to ladder graphs, Australas. J. Combin., 51, 201208, 2011.
  • A. Ahmad, M. Baca, M. F. Nadeem, On edge irregularity strength of Toeplitz graphs, U.P.B. Sci. Bull., Series A, 78(4), 155162, 2016.
  • M. Baca, Y. Bashir, M. F. Nadeem, A. Shabbir, On super edge-antimagic total labeling of Toeplitz graphs, Springer Proceedings in Mathematics & Statistics, 98 (2015), 1-11.
  • H. Enomoto, A. Lladó, T. Nakamigawa, and G. Ringel, Super edge-magic graphs, SUT J. Math., 34, 105109, 1998.
  • R. M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, The place of super edge- magic labeling among other classes of labeling, Discrete Math., 231, 153168, 2001.
  • R. M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On the super edge-magic deciency of graphs, Electron. Notes Discrete Math., 11, 2002.
  • R. M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On the super edge-magic deciency of graphs, Ars Combin., 78, 2006.
  • A. Kotzig and A. Rosa, Magic valuaton of nite graphs, Canad. Math. Bull., 13(4), 451461, 1970.
  • A. A. G. Ngurah, R. Simanjuntak and E.T. Baskoro, On the super edge-magic deciencies of graphs, Australas. J. Combin., 40, 314, 2008.
  • J.Y. Park, J.H. Choi and J.H. Bae, On super edge-magic labeling of some graphs, Bull. Korean Math. Soc., 45, No.1, 1121, 2008.
Birincil Dil en
Konular Matematik ve İstatistik
Dergi Bölümü Matematik
Yazarlar

Yazar: Ali Ahmad

Yazar: Muhammad Faisal Nadeem

Yazar: Ashok Gupta (Sorumlu Yazar)

Bibtex @araştırma makalesi { hujms439926, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {1303-5010}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {513 - 519}, doi = {}, title = {On super edge-magic deficiency of certain Toeplitz graphs}, key = {cite}, author = {Nadeem, Muhammad Faisal and Gupta, Ashok and Ahmad, Ali} }
APA Ahmad, A , Nadeem, M , Gupta, A . (2018). On super edge-magic deficiency of certain Toeplitz graphs. Hacettepe Journal of Mathematics and Statistics, 47 (3), 513-519. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/439926
MLA Ahmad, A , Nadeem, M , Gupta, A . "On super edge-magic deficiency of certain Toeplitz graphs". Hacettepe Journal of Mathematics and Statistics 47 (2018): 513-519 <http://dergipark.gov.tr/hujms/issue/38121/439926>
Chicago Ahmad, A , Nadeem, M , Gupta, A . "On super edge-magic deficiency of certain Toeplitz graphs". Hacettepe Journal of Mathematics and Statistics 47 (2018): 513-519
RIS TY - JOUR T1 - On super edge-magic deficiency of certain Toeplitz graphs AU - Ali Ahmad , Muhammad Faisal Nadeem , Ashok Gupta Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 513 EP - 519 VL - 47 IS - 3 SN - 1303-5010- M3 - UR - Y2 - 2017 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On super edge-magic deficiency of certain Toeplitz graphs %A Ali Ahmad , Muhammad Faisal Nadeem , Ashok Gupta %T On super edge-magic deficiency of certain Toeplitz graphs %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 1303-5010- %V 47 %N 3 %R %U
ISNAD Ahmad, Ali , Nadeem, Muhammad Faisal , Gupta, Ashok . "On super edge-magic deficiency of certain Toeplitz graphs". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 513-519.