Results 21 to 30 of about 45,382 (265)
AKCE International Journal of Graphs and Combinatorics, 2020 The two Zagreb indices and are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a variety of modifications of and were put forward. The present survey of these modified
Ivan Gutman +2 more
doaj +1 more source
Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
Complexity, 2021 Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present
Zhen-Mu Hong +3 more
doaj +1 more source
Random graphs with forbidden vertex degrees [PDF]
Random Structures & Algorithms, 2010 AbstractWe study the random graph Gn,λ/n conditioned on the event that all vertex degrees lie in some given subset $ {\cal S} $ of the nonnegative integers. Subject to a certain hypothesis on $ {\cal S} $, the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter $ \hat{\mu} $ given as the root of a certain ...
Geoffrey R. Grimmett, Svante Janson
openaire +4 more sources
On Triangulations with High Vertex Degree [PDF]
Annals of Combinatorics, 2008 We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}.
openaire +2 more sources
Graph realizations: Maximum degree in vertex neighborhoods
Discrete Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amotz Bar-Noy +3 more
openaire +4 more sources
Fuzzy Graph Structures with Application
Mathematics, 2019 In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples and properties.
Muzzamal Sitara +2 more
doaj +1 more source
Generalized Zagreb index of product graphs [PDF]
Transactions on Combinatorics, 2019 The generalized Zagreb index is an extension of both ordinary and variable Zagreb indices. In this paper, we present exact formulae for the values of the generalized Zagreb index for product graphs.
Mahdieh Azari
doaj +1 more source
Conjecture Involving Arithmetic-Geometric and Geometric-Arithmetic Indices
Discrete Dynamics in Nature and Society, 2022 The geometric-arithmetic (GA) index of a graph G is the sum of the ratios of geometric and arithmetic means of end-vertex degrees of edges of G. Similarly, the arithmetic-geometric (AG) index of G is defined. Recently, Vujošević et al. conjectured that a
Zainab Alsheekhhussain +3 more
doaj +1 more source
Group Degree Centrality and Centralization in Networks
Mathematics, 2020 The importance of individuals and groups in networks is modeled by various centrality measures. Additionally, Freeman’s centralization is a way to normalize any given centrality or group centrality measure, which enables us to compare individuals or ...
Matjaž Krnc, Riste Škrekovski
doaj +1 more source
A Golden Ratio Inequality for Vertex Degrees of Graphs [PDF]
The American Mathematical Monthly, 2019 Motivated by the study of the crossing number of graphs, it is shown that, for trees, the sum of the products of the degrees of the end-vertices of all edges has an upper bound in terms of the sum of all vertex degrees to the power of $ϕ^2$, where $ϕ$ is the golden ratio. The exponent $ϕ^2$ is best possible.
Fiachra Knox, Bojan Mohar, David R. Wood
openaire +2 more sources