Results 1 to 10 of about 34,637 (273)
Extremal graph theory and finite forcibility [PDF]
Electronic Notes in Discrete Mathematics, 2017 We study the uniqueness of optimal solutions to extremal graph theory problems. Our main result is a counterexample to the following conjecture of Lov´asz, which is often referred to as saying that “every extremal graph theory problem has a finitely ...
Grzesik, Andrzej +2 more
core +4 more sources
Extremal Graph Theory for Metric Dimension and Diameter [PDF]
Electronic Notes in Discrete Mathematics, 2007 A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}
C. Hern +5 more
core +9 more sources
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
doaj +2 more sources
On some interconnections between combinatorial optimization and extremal graph theory [PDF]
Yugoslav Journal of Operations Research, 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.
Cvetković Dragoš M. +2 more
doaj +3 more sources
It Is Better to Be Semi-Regular When You Have a Low Degree [PDF]
EntropyWe study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d∈3,7,
Theodore Kolokolnikov
doaj +2 more sources
On tricyclic graphs with maximum atom–bond sum–connectivity index [PDF]
HeliyonThe sum-connectivity, Randić, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees.
Sadia Noureen +5 more
doaj +2 more sources
Exponential second Zagreb index of chemical trees [PDF]
Transactions on Combinatorics, 2021 Cruz, Monsalve and Rada [Extremal values of vertex-degree-based topological indices of chemical trees, Appl. Math. Comput. 380 (2020) 125281] posed an open problem to find the maximum value of the exponential second Zagreb index for chemical ...
Selvaraj Balachandran, Tomas Vetrik
doaj +1 more source
Note on the temperature Sombor index
Vojnotehnički Glasnik, 2023 Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and several of its properties established. Methods: Combinatorial
Ivan Gutman
doaj +1 more source
Reducing the maximum degree of a graph: comparisons of bounds
Theory and Applications of Graphs, 2021 Let $\lambda(G)$ be the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree.
Peter Borg
doaj +1 more source
On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs
Frontiers in Physics, 2020 With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory.
Hongyan Lu, Zhongxun Zhu
doaj +1 more source