Quotient-4 Cordial Labeling Of Some Caterpillar And Lobster Graphs
DOI:
https://doi.org/10.53555/jaz.v44iS8.3698Keywords:
Caterpillar graph, lobster graph, Star graph, Bistar graph, Twig graph, subdivision graph, Quotient-4 cordial labeling, Quotient-4 cordial graph.Abstract
Let G (V, E) be a simple graph of order p and size q. Let φ: V (G) Z5 – {0} be a function. For each edge set E (G) define the labeling *:E (G)Z4 by *(uv)= (mod 4) where (u)(v). The function is called Quotient-4 cordial labeling of G if |vφ(i) – vφ(j)| ≤ 1, , j, ij where vφ(x) denote the number of vertices labeled with x and |eφ(k) – eφ(l)| ≤ 1, ,,, where eφ(y) denote the number of edges labeled with y. Here some caterpillar graphs such as star graph (Sn), Bistar graph (Bn,n), Pn [N] graph, Pn [No] graph, Pn [Ne] graph, Twig graph (Tm), (Pn K1, r), S(Sn), S(Bn,n), S(Pn [N]), S(Pn [No]), S(Pn [Ne]), S(Tm) and S(Pn K1, r) graph proved to be quotient-4 cordial graphs.
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References
Albert William, Indra Rajasingh and S Roy, Mean Cordial Labeling of Certain graphs, J.Comp.& Math. Sci. Vol.4 (4),274-281 (2013).
Cahit and R. Yilmaz, E3-cordial graphs, ArsCombin., 54 (2000) 119-127.
Daniel Goncalves, and Pascal Ochemb, On star and caterpillar arboricity, Discrete Mathematics, vol. 309, (2009) 3694-3702.
S. Freeda and R. S. Chellathurai, H- and H2-cordial labeling of some graphs Open J. Discrete Math., 2 (2012) 149-155.
F. Harary, Graph Theory. Narosa Publishing House Reading, New Delhi, (1988).
Joseph A. Gallian, A Dynamic survey of Graph Labeling , Twenty-first edition, December 21, 2018.
M. Murugan, Gracefully Harmonious Graphs, Matematica, vol.29, no.2 (2013) 203-214.
M. A. Seoud, and M. Anwar, On combination and permutation graphs, Utilitas Mathematica, 98, (2015) 243-255.
P.Sumathi, S.Kavitha, Quotient-4 cordial labeling for path related graphs, The International Journal of Analytical and Experimental Modal analysis, Volume XII, Issue I, January – 2020, pp. 2983-2991.
S. K. Vaidya, and N.H. Shah, On square divisor cordial graphs, Journal of Scientific Research, vol. 6, no. 3 (2014) 445-455.
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