## VERTEX COLORING EDGE WEIGHTINGS OF SOME SQUARE GRAPHS

## VERTEX COLORING EDGE WEIGHTINGS OF SOME SQUARE GRAPHS

*N. Paramaguru*

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## Abstract

A k-edge-weighting w of a graph G is an assignment of integer weight, w(e) ∈ {1,2,...,k}, to each edge e. A k-edge-weighting w induces a vertex coloring cbydefiningc(u)= E w(e)foreveryu∈V(G),whereu∼edenotethatuisan u∼e end-vertex of e. A k-edge-weighting w of a graph G is a vertex coloring of G if the in- duced coloring c is proper, i.e., c(u) ̸= c(v) for any edge uv ∈ E(G). In this paper, vertex coloring edge weighting of square of Cartesian product of paths is considered.

## Keywords

edge weighting, vertex coloring, Cartesian product