Results 11 to 20 of about 808 (83)
Algebraic Connectivity and Degree Sequences of Trees [PDF]
, 2008 We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on non-pendant vertices ...
Biyikoglu, Tuerker, Leydold, Josef
core +2 more sources
ON THE RAINBOW NEIGHBOURHOOD NUMBER OF MYCIELSKI TYPE GRAPHS
International Journal of Apllied Mathematics, 2019 A rainbow neighbourhood of a graph G is the closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one colored vertex of each color in the chromatic coloring C of G. Let G be a graph with a chromatic coloring C defined on it. The number
N. Sudev, C. Susanth, S. Kalayathankal
semanticscholar +1 more source
A Note on Quasi-Triangulated Graphs [PDF]
, 2006 A graph is quasi-triangulated if each of its induced subgraphs has a vertex which is either simplicial (its neighbors form a clique) or cosimplicial (its nonneighbors form an independent set).
Gorgos, Ion +2 more
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Some algebraic properties of a class of integral graphs determined by their spectrum
, 2021 Let $\Gamma=(V,E)$ be a graph. If all the eigenvalues of the adjacency matrix of the graph $\Gamma$ are integers, then we say that $\Gamma$ is an integral graph.
Liu, Jia-Bao +2 more
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On the 12-Representability of Induced Subgraphs of a Grid Graph
Discussiones Mathematicae Graph Theory, 2022 The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
doaj +1 more source
On the Existence of General Factors in Regular Graphs [PDF]
, 2012 Let $G$ be a graph, and $H\colon V(G)\to 2^\mathbb{N}$ a set function associated with $G$. A spanning subgraph $F$ of $G$ is called an $H$-factor if the degree of any vertex $v$ in $F$ belongs to the set $H(v)$.
Lu, Hongliang +2 more
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On the edge set of graphs of lattice paths
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 61, Page 3291-3299, 2004., 2004 This note explores a new family of graphs defined on the set of paths of the m × n lattice. We let each of the paths of the lattice be represented by a vertex, and connect two vertices by an edge if the corresponding paths share more than k steps, where k is a fixed parameter 0 = k = m + n. Each such graph is denoted by G(m, n, k).
Steven Klee, Lara Pudwell, Rick Gillman
wiley +1 more source
Maximum nullity and zero forcing of circulant graphs
Special Matrices, 2020 The zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems.
Duong Linh +4 more
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Classifying Families of Character Degree Graphs of Solvable Groups [PDF]
, 2018 We investigate prime character degree graphs of solvable groups. In particular, we consider a family of graphs $\Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion.
Bissler, Mark W., Laubacher, Jacob
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
wiley +1 more source