The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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EXTREMAL F-INDICES FOR BICYCLIC GRAPHS WITH k PENDANT VERTICES

  • Amin, Ruhul (Department of Education, Assam University) ;
  • Nayeem, Sk. Md. Abu (Department of Mathematics and Statistics, Aliah University)
  • Received : 2019.09.10
  • Accepted : 2020.11.14
  • Published : 2020.11.30
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Abstract

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.

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References

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