Results 1 to 10 of about 1,156,316 (148)
On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum ...
Shu-Guang Guo, Rong Zhang
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Acyclic 6-Colouring of Graphs with Maximum Degree 5 and Small Maximum Average Degree
Discussiones Mathematicae Graph Theory, 2013 A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . . , k} of colours such that adjacent vertices receive distinct colours.
Fiedorowicz Anna
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Wiener index in graphs with given minimum degree and maximum degree [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. In this paper we show that the well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$ on ...
Peter Dankelmann, Alex Alochukwu
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Proximity, remoteness and maximum degree in graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the average ...
Peter Dankelmann +2 more
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K-regular decomposable incidence structure of maximum degree [PDF]
Mathematica Moravica, 2023 This paper discusses incidence structures and their rank. The aim of this paper is to prove that there exists a regular decomposable incidence structure J = (P, B) of maximum degree depending on the size of the set and a predetermined rank.
Stošović Dejan +2 more
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Fractional Chromatic Number, Maximum Degree, and Girth [PDF]
SIAM Journal on Discrete Mathematics, 2021 We introduce a new method for computing bounds on the independence number and fractional chromatic number of classes of graphs with local constraints, and apply this method in various scenarios. We establish a formula that generates a general upper bound for the fractional chromatic number of triangle-free graphs of maximum degree~$ \ge 3$. This upper
Pirot, François +1 more
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On the extremal connective eccentricity index among trees with maximum degree [PDF]
Transactions on Combinatorics, 2021 The connective eccentricity index (CEI) of a graph $G$ is defined as $\xi^{ce}(G)=\sum_{v \in V(G)}\frac{d_G(v)}{\varepsilon_G(v)}$, where $d_G(v)$ is the degree of $v$ and $\varepsilon_G(v)$ is the eccentricity of $v$. In this paper, we characterize the
Fazal Hayat
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Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
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Local boxicity and maximum degree
Discrete Mathematics, 2022 The \emph{local boxicity} of a graph $G$, denoted by $lbox(G)$, is the minimum positive integer $l$ such that $G$ can be obtained using the intersection of $k$ (, where $k \geq l$,) interval graphs where each vertex of $G$ appears as a non-universal vertex in at most $l$ of these interval graphs. Let $G$ be a graph on $n$ vertices having $m$ edges. Let
Atrayee Majumder, Rogers Mathew
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The maximum likelihood degree [PDF]
American Journal of Mathematics, 2006 Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the ...
Catanese, Fabrizio +3 more
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