3-Difference cordial labeling of some path related graphs

R Ponraj, M Maria Adaickalam, R Kala


Let G be a (p, q)-graph. Let f : V(G) → {1, 2, …, k} be a map where k is an integer, 2 ≤ k ≤ p. For each edge uv, assign the label ∣f(u) − f(v)∣. f is called k-difference cordial labeling of G if ∣vf(i) − vf(j)∣ ≤ 1 and ∣ef(0) − ef(1)∣ ≤ 1 where vf(x) denotes the number of vertices labelled with x, ef(1) and ef(0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternate triangular snake, alternate quadrilateral snake, irregular triangular snake, irregular quadrilateral snake, double triangular snake, double quadrilateral snake, double alternate triangular snake, and double alternate quadrilateral snake.


Cycle; path; triangular snake; quadrilateral snake; difference cordial

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DOI: http://dx.doi.org/10.19184/ijc.2018.2.1.1


I. Cahit, Cordial Graphs: A weaker version of Graceful and Harmonious graphs, Ars combin., 23 (1987) 201-207.

J.A. Gallian, A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 19 (2016) #Ds6.

F. Harary, Graph theory, Addision wesley, New Delhi (1969).

R. Hasni, S. Matarneh, A. Azaizeh, Some results on cordiality labeling of generalized Jahangir graph, Indonesian Journal of Combinatorics, 1(2017),1-8.

R. Ponraj, S. Sathish Narayanan and R. Kala, Difference cordial labeling of graphs, Global Journal of Mathematical Sciences: Theory and Practical, 5(2013), 185-196.

R. Ponraj and M. M. Adaickalam and R.Kala, k-difference cordial labeling of graphs, International journal of mathematical combinatorics, 2(2016), 121-131.

R. Ponraj and M. M. Adaickalam, 3-difference cordial labeling of some union of graphs, Palestine journal of mathematics, 6(1)(2017), 202-210.

R. Ponraj and M. M. Adaickalam, 3-difference cordial labeling of cycle related graphs, Journal of algorithms and computation, 47 (2016), 1-10.

R. Ponraj and M. M. Adaickalam, 3-difference cordiality of some graphs, Palestine journal of mathematics, 2(2017), 141-148.

R. Ponraj and M. M. Adaickalam, 3-difference cordial labeling of corona related graphs, Submitted to the journal.

M.A.Seoudand, S.M.Salman, On difference cordial graphs, Mathematica Aeterna, 5(1) (2015), 105 - 124.


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