### k-PRIME LABELING OF UNION OF PATH GRAPH

FIRDHA - NURHIDAYAH

^{(1*)}

(1) Gadjah Mada University

(*) Corresponding Author

#### Abstract

Let G be a simple graph, connected, and undirected graph G = (V (G);E(G))

with n vertices. Injective labeling on V (G) is said to be prime if each pair of adjacent

vertices has a relative prime labels. From the development of prime labeling it is de-

veloped a new concept on kprime labeling. A kprime labeling of a graph G is an

injective function f : V (G) ! fk; k+1; k+2; :::; k +jV (G)j1g for some positive integer

k that induces a function f+ : E(G) ! N which N is the set of neightboring vertices

and on the edges of G dened by f+(uv) = gcd(f(u); f(v)), for all uv in E(G) such

that gcd(f(u); f(v)) = 1. A graph G that admits kprime labeling is called a kprime

graph. In this paper, it will be discussed about kprime labeling of some graphs such

as one point union of path graphs Pt

n for n 1 and t 5, Pn;CmmK1;r graphs for

n 3;m = 3; 4; 5, and r 2, and also Pn(Pq;K1) graphs for n 2 and q even.

#### Keywords

#### Full Text:

PDF NURHIDAYAH#### References

Chartrand, G., Lesniak, L., dan Zhang, P., Graphs & Digraphs, Fifth Edition, A Chapman & Hall Book, New York, 2011.

Gallian, J, A., A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics (2019), DS6.

Teresa, A. S. dan Vijayalakshmi, G., k−Prime Labeling of Certain Cycle Connected Graphs, Malaya Journal of Matematik, S1 (2019), 280-283.

Teresa, A, S. dan Vijayalakshmi, G., k−Prime Labeling of One Point Union of Path Graph, Procedia Computer Science, 172 (2020), 649-654.

Vaidya, S. K. dan Prajapati, U. M., Some Result on Prime and k−Prime Labeling, Journal of Mathematics Research, 3 (2011), 66-75.

DOI: https://doi.org/10.22146/jmt.66646

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