Barekeng (Mar 2024)

A PROPERLY EVEN HARMONIOUS LABELING OF SOME WHEEL GRAPH W_n FOR n IS EVEN

  • Fakhrun Nisa,
  • M. Ivan Ariful Fathoni,
  • Adika Setia Brata

DOI
https://doi.org/10.30598/barekengvol18iss1pp0553-0564
Journal volume & issue
Vol. 18, no. 1
pp. 0553 – 0564

Abstract

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A properly even harmonious labeling of a graph G with q edges is an injective mapping f from the vertices of graph G to the integers from 0 to 2q-1 such that induces a bijective mapping f* from the edges of G to {0,2,...,2q-2} defined by f*(v_iv_j)=(f(v_i)+f(v_j))(mod2q). A graph that has a properly even harmonious labeling is called a properly even harmonious graph. In this research, we will show the existence of a properly even harmonious labeling of some wheel graph W_n for n is even.

Keywords