A note on m-Zumkeller cordial labeling of graphs

Author
Patodia, Harish

Saikia, Helen K.

Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5190
10.22199/issn.0717-6279-5190
Abstract
Let G(V,E) be a graph. An m-Zumkeller cordial labeling of the graph G is defined by an injective function f:V -> N such that there exists an induced function f*:E -->{0,1} defined by f* (uv)=f(u).f(v) that satisfies the following conditions:i) For every uv in E, f*(uv)=  ii) |ef*(0)-ef*(1)|<=1where ef*(0) and ef*(1) denote the number of edges of the graph G having label 0 and 1 respectively under f*.In this paper we prove that there exist an m -Zumkeller cordial labeling of graphs viz., (i) paths (ii) cycles (iii) comb graphs (iv) ladder graphs (v) twig graphs (vi) helm graphs (vii) wheel graphs (viii) crown graphs (ix) star graphs.
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