Open Journal Systems

Adjacent Vertex Distinguishing Total Coloring Of Corona Graphs

S. Sudha K.Manikandan

crossmark logo side by side horizontal

Abstract


An adjacent vertex distinguishing total coloring of a graph  is a proper total coloring of  such that any pair of adjacent vertices have different color sets. The minimum number of colors needed for such an adjacent vertex distinguishing total coloring of  is its chromatic number and is denoted by In this paper, we have obtained the chromatic number of adjacent vertex distinguishing total coloring(AVDTC) of the following corona graphs:

(i)                  (path,  by path,  )

(ii)                (cycle,  by cycle, )

(iii)              (complete graph,  by complete graph, )

(iv)               (path,  by cycle, )

(v)                 (cycle,  by path, )

(vi)               (complete graph,  by path, )

(vii)             (complete graph,  by cycle, )

 AMS Subject Classification: 05C15


Full Text:

PDF

References


M. Behzad, “Graphs and their chromatic numbers”, Ph.D. Thesis, Michigan state university, East Lansing. (1965).

J. A. Bondy, U.S.R. Murty, “Graph theory with applications”, (1982).

X.Chen, “On the adjacent vertex distinguishing total chromatic numbers of graphs with △=3”, Discrete. Math., 308s, 4003-4007, (2008).

T.Coker, H.Johannson, “The adjacent vertex distinguishing total chromatic number” Discrete. Math., 312, 2471-2750 (2012).

D. Huang, W.Wang and C.Yan, “A note on the adjacent vertex distinguishing total Chromatic number of graphs”, Discrete.Math., 312, 3544-3546, (2012).

J. Hulgan, “Concise proofs for adjacent vertex-distinguishing total colorings”, Discrete.Math., 309, 2548-2550, (2009).

S. Sudha and K. Manikandan, “Total coloring and (k,d)-total coloring of prisms”, Mathematical Sciences International Research Journal, Vol. 3, Issue 1, pp 11-13, (2014).

S. Sudha and K. Manikandan, “Total coloring of S(n,m)-graphs”, International Journal of Scientific and Innovative Mathematical Research, Vol. 2, Issue 1, pp 16-22, (2014).

H.Wang, “On the adjacent vertex distinguishing total chromatic number of the graphs with △(G)=3”, J.Comb.Optim., 14, 87-109, (2007).

X.Zhang, H.Chen, J.Li, B.Yao, J.Wang, “On adjacent-vertex-distinguishing total coloring of graphs”, Sci.China Ser. A 48, 289-299, (2005).




DOI: http://dx.doi.org/10.15520/ajcem.2015.vol4.iss1.20.pp8-19.

Refbacks

  • There are currently no refbacks.


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