Distance Spectral Radius for a Graph to be k-Critical With Respect to [1,b]-Odd Factor

Let [Formula: see text] be a connected graph, and let [Formula: see text] and [Formula: see text] be two positive integers with [Formula: see text] (mod 2). A [Formula: see text]-odd factor of [Formula: see text] is a spanning subgraph [Formula: see text] of [Formula: see text] with [Formula: see text] (mod 2) and [Formula: see text] for every [Formula: see text]. A graph [Formula: see text] is called [Formula: see text]-critical with respect to [Formula: see text]-odd factor if [Formula: see text] contains a [Formula: see text]-odd factor for every [Formula: see text] with [Formula: see text]. Let [Formula: see text] denote the distance matrix of [Formula: see text]. The largest eigenvalue of [Formula: see text], denoted by [Formula: see text], is called the distance spectral radius of [Formula: see text]. In this paper, we prove an upper bound for [Formula: see text] in a [Formula: see text]-connected graph [Formula: see text] which guarantees [Formula: see text] to be [Formula: see text]-critical with respect to [Formula: see text]-odd factor.