Results 31 to 40 of about 605,731 (305)
An Extremal Property of Turán Graphs [PDF]
The Electronic Journal of Combinatorics, 2010 Let ${\cal F}_{n,t_r(n)}$ denote the family of all graphs on $n$ vertices and $t_r(n)$ edges, where $t_r(n)$ is the number of edges in the Turán's graph $T_r(n)$ – the complete $r$-partite graph on $n$ vertices with partition sizes as equal as possible.
Felix Lazebnik, Spencer Tofts
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Extremal graphs for edge blow-up of graphs [PDF]
Journal of Combinatorial Theory, Series B, 2022 Given a graph $H$ and an integer $p$, the {\it edge blow-up} of $H$, denoted as $H^{p+1}$, is the graph obtained from replacing each edge in $H$ by a clique of size $p+1$ where the new vertices of the cliques are all different. The Turán numbers for edge blow-up of matchings were first studied by Erdős and Moon.
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A Tabu Search Based Approach for Graph Layout [PDF]
, 2014 This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing.
Rodgers, Peter, Dib, Fadi
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Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let ℬn denote the set of bicyclic graphs without common edges and with n
Gaixiang Cai, Xing-Xing Li, Guidong Yu
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Discrete Mathematics, 1999 The \(\alpha\)-weight of an edge \(xy\) of a graph \(G\) is \(d(x)^\alpha\cdot d(y)^\alpha\) where \(d(x)\) and \(d(y)\) are the degrees of the vertices \(x\) and \(y\). The \(\alpha\)-weight of \(G\) is the sum of the \(\alpha\)-weights of its edges. The authors establish the \(\alpha\)-weight of a graph with any fixed number of edges for \(\alpha=1\)
Béla Bollobás +2 more
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On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics, 2014 The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener ...
Jianping Ou, Xing Feng, Saihua Liu
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The Number of Spanning Trees in Generalized Complete Multipartite Graphs of Fan-Type [PDF]
, 2011 Approaching topics such as connected simple graph, k-partite graph, complete graph, tree, Smarandache (E1,E2)-number of ...
Junliang Cai +3 more
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AKCE International Journal of Graphs and Combinatorics, 2023 For a connected simple graph G, the inverse degree index and forgotten index are defined as [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the degree of vertex u in G.
Mohammad Ali Manian +2 more
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Structures of Cycle Bases with Some Extremal Properties [PDF]
, 2014 In this paper, authors investigate the structures of cycle bases with extremal properties which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.
Han, Ren, Yun Bai, Han Ren, Bai, Yun
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On Acyclic Structures with Greatest First Gourava Invariant
Journal of Chemistry, 2022 Let ξ be a simple connected graph. The first Gourava index of graph ξ is defined as GO1ξ=∑μη∈Eξdμ+dη+dμdη, where dμ indicates the degree of vertex μ.
Mariam Imtiaz +4 more
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