Geodesic
Inverse degree index of graphs with a given cyclomatic number
Filomat, Tome 37 (2023) no. 27, p. 9371

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DOI

We investigate how the inverse degree index of graphs depends on their cyclomatic number. In particular, we provide sharp lower bounds on the inverse degree index over all graphs on a given number of vertices with a given cyclomatic number. We also deduce some structural properties of extremal graphs. Some open questions regarding the upper bound over the same class of graphs are discussed and some possible further developments are indicated.
DOI : 10.2298/FIL2327371A
Classification : 05C09, 05C07, 05C75, 05C92, 92E10
Keywords: Inverse degree index, unicyclic graph, bicyclic graph, cyclomatic number 
Saieed Akbari; Tomislav Došlić; Nasim Nahvi. Inverse degree index of graphs with a given cyclomatic number. Filomat, Tome 37 (2023) no. 27, p. 9371 . doi: 10.2298/FIL2327371A
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     author = {Saieed Akbari and Tomislav Do\v{s}li\'c and Nasim Nahvi},
     title = {Inverse degree index of graphs with a given cyclomatic number},
     journal = {Filomat},
     pages = {9371 },
     year = {2023},
     volume = {37},
     number = {27},
     doi = {10.2298/FIL2327371A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2327371A/}
}
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