Inverse problem for Zagreb indices
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The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.
KeywordsZagreb index First Zagreb index Second Zagreb index Forgotten index Hyper-Zagreb index
Mathematics Subject ClassificationPrimary 05C09 Secondary 05C90
This work was supported by the research fund of Uludag University, Project No. F-2015/17.
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