Results 41 to 50 of about 5,992,367 (377)
The H-Line Signed Graph of a Signed Graph [PDF]
, 2010 For standard terminology and notion in graph theory we refer the reader to Harary; the non-standard will be given in this paper as and when required.
Rangarajan, R. +2 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 +1 more
doaj +1 more source
On the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph
Open Journal of Mathematical Sciences, 2020 Let \(G=(V,E)\) be a graph. Then the first and second entire Zagreb indices of \(G\) are defined, respectively, as \(M_{1}^{\varepsilon}(G)=\displaystyle \sum_{x \in V(G) \cup E(G)} (d_{G}(x))^{2}\) and \(M_{2}^{\varepsilon}(G)=\displaystyle \sum_{\{x,y\}
H. M. Nagesh +2 more
semanticscholar +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 +2 more
doaj +1 more source
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
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
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 +7 more
doaj +1 more source
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
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 +2 more
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