Prime Coloring of Crossing Number Zero Graphs
Abstract:
In this paper, prime coloring and its chromatic number of some crossing number zero graphs are depicted and its results are vali-dated with few theorems. Prime Coloring is defined as G be a loop less and Without multiple edges with n distinct Vertices on Color class C={c1,c2,c3,…..cn} a bijection ψ:V {c1,c2,c3,…..cn} if for each edge e = cicj ,i≠j , gcd{ ψ (ci), ψ (cj)}=1, ψ (ci) and ψ (cj) receive distinct Colors. The Chromatic number of Prime coloring is minimum cardinality taken by all the Prime colors. It is denoted by η (G).
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Keywords:
Prime graph, Vertex Coloring, Prime Coloring
References:
Bondy, J. A and Murty U.S.R (1976), Graph Theory with Applications, Macmillan, London.
Galian, J. A (2009), A Dynamic Survey of Graph Labeling, Electronic Journal of Combinatorics, 16, #DS6.
Lee, S.M, Wui, J., Yeh, I(1988), On the Amalgamation Of Prime Graphs, Bull, Malaysian, Math.Soc. (Second Series), 11 , 59-67
Oleg, P. (2007), Trees are Almost Prime, Discrete Mathematics Elsevier, 307, 1455-1462. https://doi.org/10.1016/j.disc.2005.11.083
Thomas, K. (2005 ), Elementary Number Theory with Applications, Elsevier, 103-115.
Samir K. V., Udayan, M. P.(2012), Some New Results on Prime Graphs, Open Journal Of Discrete Mathematics, 2, 99-104,. http://dx.doi.org/10.4236/ojdm.2012.23019
Galian, J. A (2009), A Dynamic Survey of Graph Labeling, Electronic Journal of Combinatorics, 16, #DS6.
Lee, S.M, Wui, J., Yeh, I(1988), On the Amalgamation Of Prime Graphs, Bull, Malaysian, Math.Soc. (Second Series), 11 , 59-67
Oleg, P. (2007), Trees are Almost Prime, Discrete Mathematics Elsevier, 307, 1455-1462. https://doi.org/10.1016/j.disc.2005.11.083
Thomas, K. (2005 ), Elementary Number Theory with Applications, Elsevier, 103-115.
Samir K. V., Udayan, M. P.(2012), Some New Results on Prime Graphs, Open Journal Of Discrete Mathematics, 2, 99-104,. http://dx.doi.org/10.4236/ojdm.2012.23019
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