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Isoscalar giant resonances, being the archetypal forms of collective nuclearbehavior, have been studied extensively for decades with the goal ofconstraining bulk nuclear properties of the equation of state, as well as formodeling dynamical behaviors within stellar environments. An important suchmode is the isoscalar electric giant monopole resonance (ISGMR) that can beunderstood as a radially symmetric density vibration within the saturatednuclear volume. The field has a few key open questions, which have beenproposed and remain unresolved. One of the more provocative questions is theextra high-energy strength in the $A\approx 90$ region, which manifested inlarge percentages of the $E0$ sum rule in $^{92}$Zr and $^{92}$Mo above themain ISGMR peak. The purpose of this article is to introduce these questionswithin the context of experimental investigations into the phenomena in thezirconium and molybdenum isotopic chains, and to address, via a discussion ofpreviously published and preliminary results, the implications of recentexperimental efforts on extraction of the nuclear incompressibility from thisdata.

Where we stand on structure dependence of ISGMR in the Zr-Mo region: Implications on K_\infty