Cordial labeling of hypertrees.

Let H=(V,E) be a hypergraph with vertex set V={v1,v2,…,vn} and edge set E={e1,e2,…,em}. A vertex labeling c:V→N induces an edge labeling c∗:E→N by the rule c∗(ei)=∑vj∈eic(vj). For integers k≥2 we study the existence of labelings satisfying the following condition: every residue class modulo k occurs exactly ⌊n/k⌋ or ⌈n/k⌉ times in the sequence c(v1),c(v2),…,c(vn) and exactly ⌊m/k⌋ or ⌈m/k⌉ times in the sequence c∗(e1),c∗(e2),…,c∗(em). Hypergraph H is called k-cordial if it admits a labeling with these properties.