Integral Root Labeling of Graphs

V.L. Stella Arputha Mary; N. Nanthini

doi:https://doi.org/10.14445/22315373/IJMTT-V54P553

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 6 | Year 2018 | Article Id. IJMTT-V54P553 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P553

Integral Root Labeling of Graphs

V.L. Stella Arputha Mary, N. Nanthini

Abstract

Let 𝐺 = 𝑉,𝐸 be a graph with 𝑝 vertices and 𝑞 edges. Let 𝑓: 𝑉 → 1,2, … 𝑞 + 1 is called an Integral Root labeling if it is possible to label all the vertices 𝑣 ∈ 𝑉 with distinct elements from 1,2, … 𝑞 + 1 such that it induces an edge labeling 𝑓 +: 𝐸 → 1,2, … 𝑞 defined as 𝑓 +(𝑢𝑣) = (𝑓 𝑢 ) 2+(𝑓 𝑣 ) 2+𝑓 𝑢 𝑓(𝑣) 3 is distinct for all 𝑢𝑣 ∈ 𝐸. (i.e.) The distinct vertex labeling induces a distinct edge labeling on the graph. The graph which admits Integral Root labeling is called an Integral Root Graph. In this paper, we introduce Integral Root labeling and investigate Integral Root labeling of Path, Comb, Ladder, Triangular Snake and Quadrilateral Snake.

Keywords

Integral Root labeling, Integral Root graph, Path, Comb, Ladder, Triangular Snake, and Quadrilateral Snake.

References

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[2] F.Harary, 1988, “Graph Theory,” Narosa Publishing House Reading, New Delhi.
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[5] V.L. Stella Arputha Mary S. Navaneetha Krishnan and A. Nagarajan “ Z4p Magic labeling on some special graphs”, International journal of Mathematics and Soft Computing Vol. 3, No: 3 (2013) (61-70).
[6] V.L. Stella Arputha Mary S. Navaneetha Krishnan and A. Nagarajan “ Z4p Magic labeling for some more special graphs”, International journal of Physical Sciences, Ultra Scientist Vol. 25, No: 3 (2013) (319-326).

Citation :

V.L. Stella Arputha Mary, N. Nanthini, "Integral Root Labeling of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 6, pp. 437-447, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P553