Cacti with the smallest, second smallest, and third smallest Gutman index

Shubo Chen ()
Additional contact information
Shubo Chen: Hunan City University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 1, No 21, 327-332

Abstract: Abstract The Gutman index (also known as Schultz index of the second kind) of a graph $$G$$ G is defined as $$Gut(G)=\sum \nolimits _{u,v\in V(G)}d(u)d(v)d(u, v)$$ G u t ( G ) = ∑ u , v ∈ V ( G ) d ( u ) d ( v ) d ( u , v ) . A graph $$G$$ G is called a cactus if each block of $$G$$ G is either an edge or a cycle. Denote by $$\mathcal {C}(n, k)$$ C ( n , k ) the set of connected cacti possessing $$n$$ n vertices and $$k$$ k cycles. In this paper, we give the first three smallest Gutman indices among graphs in $$\mathcal {C}(n, k)$$ C ( n , k ) , the corresponding extremal graphs are characterized as well.

Keywords: Gutman index; Degree distance; Extremal graph; 05C12; 05C05 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-014-9743-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9743-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-014-9743-z

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().