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Displaying 341 – 360 of 363

Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems

Francis Clarke, John Hunton, Nigel Ray (2001)

Annales de l’institut Fourier

We continue our programme of extending the Roman-Rota umbral calculus to the setting of delta operators over a graded ring $E_{*}$ with a view to applications in algebraic topology and the theory of formal group laws. We concentrate on the situation where $E_{*}$ is free of additive torsion, in which context the central issues are number- theoretic questions of divisibility. We study polynomial algebras which admit the action of two delta operators linked by an invertible power series, and make related constructions...

Exterior pairs and up step statistics on Dyck paths.

Eu, Sen-Peng, Fu, Tung-Shan (2011)

The Electronic Journal of Combinatorics [electronic only]

Extraresolvability of balleans

Igor V. Protasov (2007)

Commentationes Mathematicae Universitatis Carolinae

A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.

Extrema in sequences.

Nieto, José Heber (1994)

Divulgaciones Matemáticas

Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars.

Rojo, Oscar, Medina, Luis, De Abreu, Nair M.M., Justel, Claudia (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Extremal bipartite graphs with a unique k-factor

Arne Hoffmann, Elżbieta Sidorowicz, Lutz Volkmann (2006)

Discussiones Mathematicae Graph Theory

Given integers p > k > 0, we consider the following problem of extremal graph theory: How many edges can a bipartite graph of order 2p have, if it contains a unique k-factor? We show that a labeling of the vertices in each part exists, such that at each vertex the indices of its neighbours in the factor are either all greater or all smaller than those of its neighbours in the graph without the factor. This enables us to prove that every bipartite graph with a unique k-factor and maximal size...

Extremal Crossing Numbers of Complete $k$ -Chromatic Graphs

Milan Koman (1970)

Matematický časopis

Extremal graph theory for metric dimension and diameter.

Hernando, Carmen, Mora, Mercè, Pelayo, Ignacio M., Seara, Carlos, Wood, David R. (2010)

The Electronic Journal of Combinatorics [electronic only]

Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph

Bijoya Bardhan, Mausumi Sen, Debashish Sharma (2024)

Applications of Mathematics

In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic...

Extremal Matching Energy of Complements of Trees

Tingzeng Wu, Weigen Yan, Heping Zhang (2016)

Discussiones Mathematicae Graph Theory

Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have...

Extremal Polynomials for Obtaining Bounds for Spherical Codes and Designs.

P. Boyvalenkov (1995)

Discrete & computational geometry

Extremal problems for forbidden pairs that imply hamiltonicity

Ralph Faudree, András Gyárfás (1999)

Discussiones Mathematicae Graph Theory

Let C denote the claw $K_{1, 3}$ , N the net (a graph obtained from a K₃ by attaching a disjoint edge to each vertex of the K₃), W the wounded (a graph obtained from a K₃ by attaching an edge to one vertex and a disjoint path P₃ to a second vertex), and $Z_{i}$ the graph consisting of a K₃ with a path of length i attached to one vertex. For k a fixed positive integer and n a sufficiently large integer, the minimal number of edges and the smallest clique in a k-connected graph G of order n that is CY-free (does...

Extremal problems for $t$ -partite and $t$ -colorable hypergraphs.

Mubayi, Dhruv, Talbot, John (2008)

The Electronic Journal of Combinatorics [electronic only]

Extremal Properties of the Chromatic Polynomials of Connected 3-chromatic Graphs

Ioan Tomescu (2001)

Matematički Vesnik

Extremal subsets of ${1, \dots, n}$ avoiding solutions to linear equations in three variables.

Hegarty, Peter (2007)

The Electronic Journal of Combinatorics [electronic only]

Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants ${𝒮𝒪}_{5}$ and ${𝒮𝒪}_{6}$

Wei Gao (2024)

Czechoslovak Mathematical Journal

I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by ${𝒮𝒪}_{1}, {𝒮𝒪}_{2}, \dots, {𝒮𝒪}_{6}$ . Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values...

Extremal Unicyclic Graphs With Minimal Distance Spectral Radius

Hongyan Lu, Jing Luo, Zhongxun Zhu (2014)

Discussiones Mathematicae Graph Theory

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) Cn.

Extreme distances in multicolored point sets.

Dumitrescu, Adrian, Guha, Sumanta (2004)

Journal of Graph Algorithms and Applications

Extreme geodesic graphs

Gary Chartrand, Ping Zhang (2002)

Czechoslovak Mathematical Journal

For two vertices $u$ and $v$ of a graph $G$ , the closed interval $I [u, v]$ consists of $u$ , $v$ , and all vertices lying in some $u -- v$ geodesic of $G$ , while for $S \subseteq V (G)$ , the set $I [S]$ is the union of all sets $I [u, v]$ for $u, v \in S$ . A set $S$ of vertices of $G$ for which $I [S] = V (G)$ is a geodetic set for $G$ , and the minimum cardinality of a geodetic set is the geodetic number $g (G)$ . A vertex $v$ in $G$ is an extreme vertex if the subgraph induced by its neighborhood is complete. The number of extreme vertices in $G$ is its extreme order $e x (G)$ . A graph $G$ is an extreme geodesic...

Extremely Irregular Graphs

M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)

Kragujevac Journal of Mathematics

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