Results 41 to 50 of about 5,977,266 (359)

Unavoidable induced subgraphs in large graphs with no homogeneous sets [PDF]

, 2015
A homogeneous set of an $n$-vertex graph is a set $X$ of vertices ($2\le |X|\le n-1$) such that every vertex not in $X$ is either complete or anticomplete to $X$. A graph is called prime if it has no homogeneous set.
Diestel, Ding, Kwon, Lovász, Maria Chudnovsky, Möhring, Oporowski, Paul Seymour, Ringi Kim, Sang-il Oum, Sumner, Sumner, Zverovich   +12 more
core   +1 more source

Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph

Complex, 2020
Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S.
Jia-bao Liu, A. Zafari
semanticscholar   +1 more source

On-line rankings of graphs

Discrete Mathematics, 2000
Let \(G= (V,E)\) be a simple graph. A vertex \(k\)-ranking of \(G\) is a proper vertex coloring \(\varphi: V\to\{1,\dots, k\}\) such that every path in \(G\) with endvertices \(x\) and \(y\) of the same color \(\varphi(x)= \varphi(y)\) contains a vertex \(z\) with higher color \(\varphi(z)> \varphi(x)\).
I. Schiermeyer, Zs. Tuza, Margit Voigt
openaire   +3 more sources

Expert interpretation of bar and line graphs: The role of graphicacy in reducing the effect of graph format. [PDF]

, 2015
The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987) has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on ...
Ali, Ali, Anderson, Aron, Carpenter, Chase, Cleveland, Crutcher, Culbertson, De Groot, Ericsson, Fox, Friel, Friel, Koedinger, Kosslyn, Kosslyn, Larkin, Newell, Norman, Palmer, Peden, Peebles, Peebles, Peebles, Peebles, Pinker, Ratwani, Schutz, Shah, Shah, Shah, Wertheimer, Zacks   +33 more
core   +2 more sources

Characterizations of the Family of All Generalized Line Graphs—Finite and Infinite—and Classification of the Family of All Graphs Whose Least Eigenvalues ≥ −2

Discussiones Mathematicae Graph Theory, 2013
The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (
Vijayakumar Gurusamy Rengasamy
doaj   +1 more source

On an edge partition and root graphs of some classes of line graphs

Electronic Journal of Graph Theory and Applications, 2017
The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line ...
K Pravas, A. Vijayakumar
doaj   +1 more source

Drawing Planar Graphs with Few Geometric Primitives [PDF]

, 2017
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path ...
A Igamberdiev, A Schulz, D Mondal, DR Lick, GA Wade, H Fraysseix de, H Fraysseix de, H Zhang, N Bonichon, S Chaplick, S Chaplick, S Durocher, S Felsner, V Dujmović   +13 more
core   +4 more sources

Local edge coloring of graphs

AKCE International Journal of Graphs and Combinatorics, 2021
Let be a graph. A local edge coloring of G is a proper edge coloring such that for each subset S of E(G) with there exist edges such that where ns is the number of copies of P3 in the edge induced subgraph The maximum color assigned by a local edge ...
P. Deepa, P. Srinivasan, M. Sundarakannan   +2 more
doaj   +1 more source

Under which conditions is λ″(G)=κ″(L(G))?

AKCE International Journal of Graphs and Combinatorics, 2023
In this paper we show that if G is a connected graph such that [Formula: see text], [Formula: see text] and [Formula: see text] then [Formula: see text] exists and [Formula: see text] if and only if G is not super-[Formula: see text]. We also obtain some
Farnaz Soliemany, Mohsen Ghasemi, Rezvan Varmazyar   +2 more
doaj   +1 more source

The treewidth of line graphs

Journal of Combinatorial Theory, Series B, 2018
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to determining the minimum vertex congestion of an embedding of $G$ into a tree.
Daniel J. Harvey, David R. Wood
openaire   +3 more sources