Results 1 to 10 of about 18,692 (262)
Some remarks on the sum of powers of the degrees of graphs [PDF]
Transactions on Combinatorics, 2021 Let $G=(V,E)$ be a simple graph with $n\ge 3$ vertices, $m$ edges and vertex degree sequence $\Delta=d_1 \ge d_2 \ge \cdots \ge d_n=\delta>0$. Denote by $S=\{1, 2,\ldots,n\}$ an index set and by $J=\{I=(r_1, r_2,\ldots,r_k) \, | \, 1\le ...
Emina Milovanovic +2 more
doaj +1 more source
Toughness and Vertex Degrees [PDF]
Journal of Graph Theory, 2012 AbstractWe study theorems giving sufficient conditions on the vertex degrees of a graph G to guarantee G is t‐tough. We first give a best monotone theorem when , but then show that for any integer , a best monotone theorem for requires at least nonredundant conditions, where grows superpolynomially as .
Bauer, D. +4 more
openaire +4 more sources
Vertex degrees close to the average degree
Discrete Mathematics, 2023 Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular, for $d_+\in \left(\sqrt{dn},n-1\right]$, we show the existence of a vertex in $G$ of degree between $d_+-\left ...
Pardey, Johannes, Rautenbach, Dieter
openaire +3 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
Estimating vertex-degree-based energies [PDF]
Vojnotehnicki glasnik, 2022 Introduction/purpose: In the current literature, several dozens of vertex-degree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is the energy (= sum of the absolute values of the eigenvalues) of the respective VDB matrix.
openaire +2 more sources
First and Second Zagreb Coindices for Chains of Cycles [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 —The graphs which are used in this paper are simple, finite and undirected. The first and second Zagreb indices for every non-adjacent vertices (also called first and second Zagreb coindices) are dependent only on the non-adjacent vertices degrees ...
Ammar Waadallah, Ahmed Ali
doaj +1 more source
Note on the Reformulated Zagreb Indices of Two Classes of Graphs
Journal of Chemistry, 2020 The reformulated Zagreb indices of a graph are obtained from the original Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of its two end vertices minus 2.
Tongkun Qu +3 more
doaj +1 more source
ON THE DISTRIBUTION OF THE SECOND DEGREES OF CONFIGURATION GRAPHS VERTICES
Transactions of the Karelian Research Centre of the Russian Academy of Sciences, 2019 The object is configuration graphs with N vertices, numbered from 1 to N, whosevertex degrees are independent identically distributed random variables.
Elena Khvorostyanskaya
doaj +1 more source
On subgroups product graph of finite groups [PDF]
BIO Web of ConferencesThis paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n.
Abd Shakir Jawad, Shelash Hayder B.
doaj +1 more source
Self-locking degree-4 vertex origami structures [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016 A generic degree-4 vertex (4-vertex) origami possesses one continuous degree-of-freedom for rigid folding, and this folding process can be stopped when two of its facets bind together. Such facet-binding will induceself-lockingso that the overall structure stays at a pre-specified configuration without additional locking elements or actuators.
Hongbin Fang, Suyi Li, K. W. Wang
openaire +3 more sources