Results 21 to 30 of about 34,683 (312)
Problems in extremal graphs and poset theory
, 2018 In this dissertation, we present three different research topics and results regarding such topics. We introduce partially ordered sets (posets) and study two types of problems concerning them-- forbidden subposet problems and induced-poset-saturation problems. We conclude by presenting results obtained from studying vertex-identifying codes in graphs.
Shanise Walker
openalex +5 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
Extremal Combinatorics in Geometry and Graph Theory
, 2013 We study a problem in extremal geometry posed by Paul Erdos and George Szekeres in 1935. This problem is to find the smallest positive integer N(n) such that every point set in general position (no three on a line) of N(n) points contains the vertex set of a convex n-gon.
Jonathan E. Beagley
openalex +2 more sources
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
On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number
AIMS Mathematics, 2021 Nowadays, it is an important task to find extremal values on any molecular descriptor with respect to different graph parameters. In a molecular graph, the vertices represent the atoms and the edges represent the chemical bonds in the terms of graph ...
Xiaoling Sun, Yubin Gao, Jianwei Du
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
, 2020 We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the resulting set is ...
Grzesik, Andrzej +2 more
core +2 more sources
A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +3 more
doaj +2 more sources
Triangles in Ks-saturated graphs with minimum degree t
Theory and Applications of Graphs, 2020 For $n \geq 15$, we prove that the minimum number of triangles in an $n$-vertex $K_4$-saturated graph with minimum degree 4 is exactly $2n-4$, and that there is a unique extremal graph.
Craig Timmons +3 more
doaj +1 more source