A Note on the Kirchhoff and Additive Degree-Kirchhoff Indices of Graphs Academic Article

abstract

• Abstract Two resistance-distance-based graph invariants, namely, the Kirchhoff index and the additive degree-Kirchhoff index, are studied. A relation between them is established, with inequalities for the additive degree-Kirchhoff index arising via the Kirchhoff index along with minimum, maximum, and average degrees. Bounds for the Kirchhoff and additive degree-Kirchhoff indices are also determined, and extremal graphs are characterised. In addition, an upper bound for the additive degree-Kirchhoff index is established to improve a previously known result.

authors

• Klein, Douglas

published proceedings

• ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES

author list (cited authors)

• Yang, Y., & Klein, D. J.

citation count

• 7

complete list of authors

• Yang, Yujun||Klein, Douglas J

publication date

• June 2015

publisher

• DE GRUYTER  Publisher

published in

• Zeitschrift fur Naturforschung A  Journal

keywords

• Additive Degree-kirchhoff Index
• Average Degree
• Kirchhoff Index
• Maximum Degree
• Minimum Degree
• Resistance Distance

Digital Object Identifier (DOI)

• 10.1515/zna-2014-0274

start page

• 459

end page

• 463

volume

• 70

issue

• 6

URL

• http://dx.doi.org/10.1515/zna-2014-0274