Carriers of diffuse interstellar bands (DIBs) still need to be identified. In a recent paper, we reported a correlation between the DIB wavelength and the apparent UV resilience (or boost) of their carriers. We proposed that this might be an indication of the important role of conjugated elongated molecules among the DIB carriers. The aim of this paper is to further understand the origin of this correlation. The analysis of 509 optical DIBs on the lines of sight of HD 183143 and/or HD 204827 reported in the literature shows that this correlation mainly implies the 386 narrow DIBs with a band width < 1.1 A, which include most of the identified DIBs of the C2 and zeta families, while the majority of the 123 broader DIBs, including the identified sigma DIBs, do not display such a correlation. We present a possible origin of this correlation from very strong bands of large conjugated elongated molecules, such as carbon chains, polyacenes, or other catacondensed polycyclic aromatic hydrocarbons. The total amount of carbon contained in all the carriers of these narrow DIBs is a very small fraction of the interstellar carbon if their oscillator strengths are <~1. The amount of carbon locked in the carriers of the broader DIBs is higher, especially if their oscillator strengths are significantly weaker.
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