Complete characterization of bicyclic graphs with minimal Kirchhoff index

DOI10.1016/j.dam.2015.07.001zbMath1329.05159OpenAlexW1022727114MaRDI QIDQ906436

N. E. Zubov

Publication date: 21 January 2016

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

Full work available at URL: https://doi.org/10.1016/j.dam.2015.07.001

zbMATH Keywords

extremal graphsWiener indexresistance distanceKirchhoff indexbicyclic graphs\(\varTheta\)-type graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Distance in graphs (05C12) Connectivity (05C40)

Related Items (34)

On the minimum Kirchhoff index of graphs with a fixed number of cut vertices ⋮ Maximum resistance-Harary index of cacti ⋮ On the minimum Kirchhoff index of unicyclic graphs with given girth and diameter ⋮ A discrete random walk on the hypercube ⋮ On the sharp lower bounds of Zagreb indices of graphs with given number of cut vertices ⋮ Kirchhoff index and degree Kirchhoff index of complete multipartite graphs ⋮ Statistical analyses of a class of random pentagonal chain networks with respect to several topological properties ⋮ Computation of resistance distance with Kirchhoff index of body centered cubic structure ⋮ The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications ⋮ New Bounds for Some Topological Indices ⋮ Fractional Herglotz variational problems with Atangana-Baleanu fractional derivatives ⋮ Zagreb indices and multiplicative Zagreb indices of Eulerian graphs ⋮ Resistance distance and Kirchhoff index for a class of graphs ⋮ Resistance distances in corona and neighborhood corona networks based on Laplacian generalized inverse approach ⋮ Further results on resistance distance and Kirchhoff index in electric networks ⋮ On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs ⋮ Minimizing Kirchhoff index among graphs with a given vertex bipartiteness ⋮ The (degree-) Kirchhoff indices in random polygonal chains ⋮ On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations ⋮ Cacti with maximum eccentricity resistance-distance sum ⋮ Bicyclic graphs with extremal cover cost ⋮ The domination complexity and related extremal values of large 3D torus ⋮ Comparison of the Wiener and Kirchhoff indices of random pentachains ⋮ ON TOPOLOGICAL PROPERTIES OF PLANE GRAPHS BY USING LINE OPERATOR ON THEIR SUBDIVISIONS ⋮ FOURTH ATOM-BOND CONNECTIVITY INDEX AND FIFTH ARITHMETIC-GEOMETRIC INDEX OF CONVEX POLYTOPES BY USING LINE OPERATOR ⋮ On the degree Kirchhoff index of unicyclic graphs ⋮ Number of spanning trees in the sequence of some graphs ⋮ Upper and lower bounds for the Kirchhoff index of the \(n\)-dimensional hypercube network ⋮ Maximum Detour-Harary index for some graph classes ⋮ Unnamed Item ⋮ Resistance distance in \(H\)-join of graphs \(G_1,G_2,\dots,G_k\) ⋮ Cost-optimized data placement strategy for social network with security awareness in edge-cloud computing environment ⋮ Identifying vital nodes in hypernetwork based on local centrality ⋮ Sharp upper bounds for multiplicative Zagreb indices of bipartite graphs with given diameter

Cites Work

• Asymptotic Laplacian-energy-like invariant of lattices
• On the Kirchhoff index of the complement of a bipartite graph
• Comparison theorems on resistance distances and Kirchhoff indices of \(S,T\)-isomers
• Asymptotic incidence energy of lattices
• Bounds for the Kirchhoff index via majorization techniques
• Resistance distance in subdivision-vertex join and subdivision-edge join of graphs
• On the Kirchhoff index of graphs with diameter 2
• On extremal bipartite unicyclic graphs
• A recursion formula for resistance distances and its applications
• The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs
• The Kirchhoff index of subdivisions of graphs
• Some physical and chemical indices of clique-inserted lattices
• A note on ‘some physical and chemical indices of clique-inserted lattices’
• The curl of a weighted network
• ON THE NORMALISED LAPLACIAN SPECTRUM, DEGREE-KIRCHHOFF INDEX AND SPANNING TREES OF GRAPHS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Complete characterization of bicyclic graphs with minimal Kirchhoff index