Results 31 to 40 of about 1,939,159 (235)

On the planarity of line Mycielskian graph of a graph

Ratio Mathematica, 2020
The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e.
Keerthi G. Mirajkar, Anuradha V Deshpande   +1 more
doaj   +1 more source

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

On a Combinatorial Approach to Studying the Steiner Diameter of a Graph and Its Line Graph

Mathematics, 2022
In 1989, Chartrand, Oellermann, Tian and Zou introduced the Steiner distance for graphs. This is a natural generalization of the classical graph distance concept. Let Γ be a connected graph of order at least 2, and S\V(Γ).
Hongfang Liu, Zhizhang Shen, Chenxu Yang, Kinkar Chandra Das   +3 more
doaj   +1 more source

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

Characterizing ‐perfect line graphs [PDF]

International Transactions in Operational Research, 2016
AbstractThe aim of this paper is to study the Lovász‐Schrijver PSD operator applied to the edge relaxation of the stable set polytope of a graph. We are particularly interested in the problem of characterizing graphs for which generates the stable set polytope in one step, called ‐perfect graphs.
Escalante, Mariana Silvina, Nasini, Graciela Leonor, Wagler, Annegret Katrin   +2 more
openaire   +5 more sources

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

ConvGraph: Community Detection of Homogeneous Relationships in Weighted Graphs

Mathematics, 2021
This paper proposes a new method, ConvGraph, to detect communities in highly cohesive and isolated weighted graphs, where the sum of the weights is significantly higher inside than outside the communities.
Héctor Muñoz, Eloy Vicente, Ignacio González, Alfonso Mateos, Antonio Jiménez-Martín   +4 more
doaj   +1 more source

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

Morphing Planar Graph Drawings Optimally [PDF]

, 2014
We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound.
C. Erten, C. Friedrich, C. Gotsman, C. Thomassen, C. Thomassen, N. Chiba, P. Angelini, S.H. Hong, S.S. Cairns, V. Surazhsky, V. Surazhsky   +10 more
core   +1 more source

On the r-dynamic coloring of some fan graph families

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the
Falcón Raúl M., Venkatachalam M., Gowri S., Nandini G.   +3 more
doaj   +1 more source