Szeged, PI and Mostar indices are some of the most investigated distance‐based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged‐like topological indices. In this paper, we formally introduce the concept of a general Szeged‐like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged‐like topological index for any strength‐weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well‐known families of molecular graphs. In particular, closed‐form formulas for some subfamilies of these graphs are deduced.

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A catacondensed even ring system (shortly CERS) is a simple bipartite 2-connected outerplanar graph with all vertices of degree 2 or 3. In this paper, we investigate the resonance graphs (also called Z-transformation graphs) of CERS and firstly show that two even ring chains are resonantly equivalent iff their resonance graphs are isomorphic. As the main result, we characterize CERS whose resonance graphs are daisy cubes. In this way, we greatly generalize the result known for kinky benzenoid graphs. Finally, some open problems are also presented. IntroductionCatacondensed even ring systems (CERS), which were introduced in [8], are a subfamily of bipartite outerplanar graphs and have an important role in chemistry since they represent various classes of molecular graphs, i.e. catacondensed benzenoid graphs [6], phenylenes, α-4-catafusenes [4], cyclooctatetraenes [9], catacondensed C 4 C 8 systems [5], etc. In this paper, we investigate the resonance graphs of CERS, since the resonance graphs model interactions among the perfect matchings (in chemistry known as Kekulé structures) of a given CERS. In mathematics, resonance graphs were introduced for benzenoid graphs by Zhang et. al. [13] under the name Z-transformation graphs. Moreover, this concept has been independently introduced by chemists. Later, the concept was generalized so that the resonance graph was defined and investigated also for other families of graphs [2,3,10,12].In [8] it was proved that the resonance graph of a CERS is a median graph and it was described how it can be isometrically embedded into a hypercube (for the definition of a median graph see [3,8]). These results were applied in [1], where the binary coding procedure for the perfect matchings of a CERS was established. Moreover, the concept of resonantly equivalent CERS was introduced and it was shown that if two CERS are resonantly equivalent, then their resonance graphs are isomorphic. However, the backward implication remained open and we address this problem in Section 3. More precisely, we prove that it is true for even ring chains, but not in general, since we give an example of two CERS which are not resonantly equivalent and have isomorphic resonance graphs.Daisy cubes were introduced in [7] as a subfamily of partial cubes. It was proved in [14] that the resonance graphs of kinky benzenoid graphs are daisy cubes. In Section 4, we generalize this result to all CERS. Moreover, we characterize the CERS whose resonance graphs are daisy cubes.