  In this article, we introduce the class $B$-Nekrasov tensor in the context of
tensor complementarity problem. We study some tensor theoretic properties. We
show that the class of B-Nekrasov tensor contains the class of Nekrasov
$Z$-tensor with positive diagonal entries. We present a necessary and
sufficient condition for a $B$-Nekrasov tensor. We show that the class of
$P$-tensor contains the class of $B$-Nekrasov tensor.
  Keywords: Tensor complementarity problem, $P$-tensors, Nekrasov tensors,
Nekrasov $Z$-tensor, $B$-Nekrasov tensors, Nonsingular $H$-tensor, Diagonally
dominant tensor.
