Square Sum And Square Difference Labelings Of Semitotal-block Graph For Some Class Of Graphs

Keerthi G. Mirajkar, Priyanka Sthavarmath G.


A graph G is said to be square sum and square difference labeling, if there exists a bijection f from V (G) to {1, 2, 3, ..., (p − 1)} which induces the injective function f ∗ from E(G) to N, defined by f ∗(uv) = f(u)2 + f(v)2 and f ∗(uv) = f(u)2 − f(v)2 respectively, for each uv ∈ E(G) and the resulting edges are distinctly labeled. G is said to be square sum and square difference graph, if it asdmits a square sum and square difference labeling respectively. The present work investigates, square sum and square difference labeling
of semitotal-block graph for some class of graphs which are proved using number theory concept.


Square Sum Labeling (SSL), Square Difference Labeling( SDL) , Semitotal-Block Graph, Comb Graph, Crown Graph, and Friendship Graph.

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J. Babujee and S. Babitha. On square sum labeling in graphs. Int.Rev.Fuzzy Math., 7(2):81–87, 2012.

J. Bondy and U. Murthy. Graph Theory With Applications. Elsevier Science, 1976.

D. Burton. Elementary Number Theory. Tata Magraw Hill, 2006. F.Harary. Graph Theory. Addison-Wesleyl, 1969.

J. A. Gallian. A dynamic survey of graph labeling. Electronic Journal of combinatorics, (DynamicSurveys), 2020.

G. Ghodasara and M. Patel. Innovative results on square sum labeling of graphs. J. Graph Label., 4(1):15–24, 2018.

G. Ghodasara and M. J. Patel. Some bistar related square sum graphs. International Journal of Mathematics Trends and Technology, 47(3):172–177, 2017.

V. Govindan and S. Dhivya. Square sum and square difference labeling of graphs. J. Appl.Sci. Comput., 4(2):1687–1692, 2019.

V. R. Kulli. The semitotal-block graph and the total-block graph of a graph. 1976.

R. Sebastian and K. Germina. Square sum labeling of class of planar graphs. Proyecciones (Antofagasta), 34(1):55–68, 2015.

J. Shiama. Square difference labeling for some graphs. International journal of computer applications, 44(4):30–33, 2012.

DOI: http://dx.doi.org/10.23755/rm.v47i0.804


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