• Corpus ID: 208268540

A relaxed version of \v{S}olt\'{e}s's problem and cactus graphs

  title={A relaxed version of \v\{S\}olt\'\{e\}s's problem and cactus graphs},
  author={Jan Bok and Nikola Jedlivckov'a and Jana Maxov'a},
The Wiener index is a graph parameter originating from chemical graph theory. It is defined as the sum of the lengths of the shortest paths between all unordered pairs of vertices in a given graph. In 1991, Šoltés [12] posed the following problem regarding the Wiener index. Find all graphs such that its Wiener index is preserved upon removal of any vertex. The problem is far from being solved and to this day, only one graph with such property is known — the cycle graph on 11 vertices. In this… 

Figures and Tables from this paper


Graphs preserving Wiener index upon vertex removal
Graphs whose Wiener index does not change when a specific vertex is removed
Wiener Index of Trees: Theory and Applications
The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. The paper outlines the results known for W of trees: methods for computation of W and combinatorial
Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons
A topological index Z is proposed for a connected graph G representing the carbon skeleton of a saturated hydrocarbon. The integer Z is the sum of a set of the numbers p(G,k), which is the number of
On the Wiener Polarity Index
The Wiener polarity index WP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between
Mathematical aspects of Wiener index
Some results, conjectures and problems on this molecular descriptor, defined as the sum of distances between all unordered pairs of vertices in a graph are summarized.
The Structure of Complex Networks: Theory and Applications
The second part of this book is devoted to the analysis of genetic, protein residue, protein-protein interaction, intercellular, ecological and socio-economic networks, including important breakthroughs as well as examples of the misuse of structural concepts.
A Survey on Graphs Extremal with Respect to Distance-Based Topological Indices
This survey outlines results on graphs extremal with respect to distance–based indices, with emphasis on the Wiener index, hyper–Wiener index, Harary index, Wiener polarity index, reciprocal
Transmission in graphs: A bound and vertex removing