Results 21 to 30 of about 1,844,339 (310)

Solutions of Detour Distance Graph Equations

Sensors, 2022
Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs.
S. Celine Prabha, M. Palanivel, S. Amutha, N. Anbazhagan, Woong Cho, Hyoung-Kyu Song, Gyanendra Prasad Joshi, Hyeonjoon Moon   +7 more
doaj   +1 more source

Energy of line graphs

Linear Algebra and its Applications, 2010
AbstractThe energy of a graph is equal to the sum of the absolute values of its eigenvalues. The energy of a matrix is equal to the sum of its singular values. We establish relations between the energy of the line graph of a graph G and the energies associated with the Laplacian and signless Laplacian matrices of G.
Gutman, Ivan, Robbiano M., Andrade, Enide, Cardoso, Domingos, Medina, Luis, Rojo O.   +5 more
openaire   +8 more sources

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

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

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

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

Edge homogeneous colorings [PDF]

Opuscula Mathematica, 2022
We explore four kinds of edge colorings defined by the requirement of equal number of colors appearing, in particular ways, around each vertex or each edge.
Tomáš Madaras, Alfréd Onderko, Thomas Schweser   +2 more
doaj   +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