Results 21 to 30 of about 742 (250)
A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices
Axioms, 2023 The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline ...
Rashad Ismail +4 more
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On a problem in extremal graph theory
Journal of Combinatorial Theory, Series B, 1977 From the authors introduction. Let \(G(n,m)\) denote a graph \((V,E)\) with \(n\) vertices and \(m\) edges and \(K_1\) a complete graph with \(i\) vertices. \textit{P.Turán} proved that every \(G(n,T(n,k))\) contains a \(K_k\), where \[ T(n,k) = \frac{k-2}{2(k-1)}(n^2-r^2)+\binom r2+1, \] \(r\equiv n(\mod k-1)\) and \(0\leq r\leq k-2\).
D. T. Busolini, Paul Erdös
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Compactness results in extremal graph theory [PDF]
Combinatorica, 1982 (From the authors' abstract:) ``Let \(L\) be a given family of \dots 'prohibited graphs'. Let \(\text{ex}(n,L)\) denote the maximum number of edges a simple graph of order n can have without containing subgraphs from \(L\). A typical extremal graph problem is to determine \(\text{ex}(n,L)\), or, at least, to find good bounds on it.
Paul Erdös, Miklós Simonovits
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Two Extremal Problems in Graph Theory
The Electronic Journal of Combinatorics, 1994 We consider the following two problems. (1) Let $t$ and $n$ be positive integers with $n\geq t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that contains neither $K_t$ nor $K_{t,t}$ as a subgraph. (2) Let $r$, $t$ and $n$ be positive integers with $n\geq rt$ and $t\geq 2$. Determine the maximum number of edges of a graph of
Richard A. Brualdi, Stephen Mellendorf
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An extremal problem in graph theory II [PDF]
Journal of the Australian Mathematical Society, 1980 AbstractWe contine our study of the following combinatorial problem: What is the largest integer N = N (t, m, p) for which there exists a set of N people satisfying the following conditions: (a) each person speaks t languages, (b) among any m people there are two who speak a common language and (c) at most p speak a common language.
Abbott, H. L. +2 more
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Hypergraphs with infinitely many extremal constructions
Discrete Analysis, 2023 Hypergraphs with infinitely many extremal constructions, Discrete Analysis 2023:18, 34 pp. A fundamental result in extremal graph theory, Turán's theorem, states that the maximal number of edges of a graph with $n$ vertices that does not contain a ...
Jianfeng Hou +4 more
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Complexity, 2021 Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use.
Muhammad Asif +5 more
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An advance in infinite graph models for the analysis of transportation networks
International Journal of Applied Mathematics and Computer Science, 2016 This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph.
Cera Martín, Fedriani Eugenio M.
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Asymptotic Structure for the Clique Density Theorem
Discrete Analysis, 2020 Asymptotic structure for the clique density theorem, Discrete Analysis 2020:19, 26 pp. Turán's theorem, which is regarded as the "first" result in extremal graph theory, is the statement that the $K_r$-free graph on $n$ vertices with the largest number ...
Jaehoon Kim +3 more
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Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices [PDF]
Yugoslav Journal of Operations Research, 2019 The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G.
Devillez Gauvain +3 more
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