On the maximum and minimum Zagreb indices of graphs with connectivity at most \(k\)

DOI10.1016/j.aml.2009.08.015zbMath1201.05028OpenAlexW1998944033MaRDI QIDQ710976

Haibing Zhou, Shuchao Li

Publication date: 25 October 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.08.015

zbMATH Keywords

connectivitytopological indexZagreb indexedge connectivity

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Applications of graph theory (05C90) Planar graphs; geometric and topological aspects of graph theory (05C10) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (23)

The first and the second Zagreb indices of the generalized Mycielskian of graphs ⋮ On extremal bipartite graphs with a given connectivity ⋮ Extremal graphs for Estrada indices ⋮ On the sharp lower bounds of Zagreb indices of graphs with given number of cut vertices ⋮ Sharp bounds for the Zagreb indices of bicyclic graphs with \(k\)-pendant vertices ⋮ Sharp upper bounds for Zagreb indices of bipartite graphs with a given diameter ⋮ On the reduced second Zagreb index of trees ⋮ Sharp upper bounds on Zagreb indices of bicyclic graphs with a given matching number ⋮ On the extremal cacti of given parameters with respect to the difference of Zagreb indices ⋮ The Zagreb indices of graphs with a given clique number ⋮ Sharp bounds on the zeroth-order general randić indices of conjugated bicyclic graphs ⋮ Unnamed Item ⋮ Sharp bounds of the Zagreb indices of \(k\)-trees ⋮ On the monotonicity of topological indices and the connectivity of a graph ⋮ The Zagreb indices of four operations on graphs ⋮ The Zagreb indices of graphs based on four new operations related to the lexicographic product ⋮ On the spectral radius and energy of the weighted adjacency matrix of a graph ⋮ Sharp bounds on the reduced second Zagreb index of graphs with given number of cut vertices ⋮ The Laplacian-energy like of graphs ⋮ Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number ⋮ Sharp bounds for Zagreb indices of maximal outerplanar graphs ⋮ Extremal tetracyclic graphs with respect to the first and second Zagreb indices ⋮ Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k

Cites Work

• On the connectivity index of trees
• Extreme values of the sum of squares of degrees of bipartite graphs
• An upper bound on the sum of squares of degrees in a graph
• Maximizing the sum of the squares of the degrees of a graph
• Extremal \((n,n + 1)\)-graphs with respected to zeroth-order general Randić index
• Sharp bounds for the second Zagreb index of unicyclic graphs
• Sums of powers of the degrees of a graph
• Trees of extremal connectivity index
• Minimizer graphs for a class of extremal problems
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