Results 51 to 60 of about 5,992,367 (377)
Discrete Mathematics, 2009 AbstractBrualdi and Shanny [R.A. Brualdi, R.F. Shanny, Hamiltonian line graphs, J. Graph Theory 5 (1981) 307–314], Clark [L. Clark, On hamitonian line graphs, J. Graph Theory 8 (1984) 303–307] and Veldman [H.J. Veldman, On dominating and spanning circuits in graphs, Discrete Math.
Minmin Zong, Liming Xiong
openaire +2 more sources
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 +2 more
doaj +1 more source
Hamilton cycles in 5-connected line graphs [PDF]
, 2011 A conjecture of Carsten Thomassen states that every 4-connected line graph is hamiltonian. It is known that the conjecture is true for 7-connected line graphs.
Kaiser, Tomáš, Vrána, Petr
core +2 more sources
Biomedical Interaction Prediction with Adaptive Line Graph Contrastive Learning
Mathematics, 2023 Biomedical interaction prediction is essential for the exploration of relationships between biomedical entities. Predicted biomedical interactions can help researchers with drug discovery, disease treatment, and more.
Shilin Sun +3 more
doaj +1 more source
Electronic Notes in Discrete Mathematics, 2010 Abstract We observe that ω ( G ) + χ ( S ( G → ) ) = n = ω ( S ( G → ) ) + χ ( G ) for any graph G with n vertices, where G → is any acyclic orientation of G and where S ( G → ) is the (complement of the) auxiliary line graph introduced in [Cornaz, D., and Jost, V., A one-to-one ...
Cornaz, Denis, Meurdesoif, Philippe
openaire +2 more sources
CMMSE 18: geometric-arithmetic index and line graph [PDF]
Journal of Mathematical Chemistry, 2019 The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $$GA_1$$GA1 and characterize ...
D. Pestana, J. M. Sigarreta, E. Tourís
semanticscholar +1 more source
On Automorphisms of Line-graphs
European Journal of Combinatorics, 1980 Let α be an automorphism of the line-graph of the r-uniform hypergraph ℋ with n points. If the valencies of ℋ v(x1) ⩽ v(x2) ⩽ ⋯ ⩽ v(xn) and υ(x2)≥υ(n,r)andυ(x2r)>υ(n,r)=(r−1n−1)−(r−1n−r−1)+1, then for n > 4r a is induced by an automorphism of ℋ (i.e.
Zoltán Füredi, Péter L. Erdös
openaire +2 more sources
The competition number of a generalized line graph is at most two
, 2012 In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one.
Park, Boram, Sano, Yoshio
core +3 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 +12 more
core +1 more source
Discrete Mathematics, 2000 AbstractA (vertex) k-ranking of a graph G=(V,E) is a proper vertex coloring ϕ:V→{1,…,k} such that each path with endvertices of the same color i contains an internal vertex of color ⩾i+1. In the on-line coloring algorithms, the vertices v1,…,vn arrive one by one in an unrestricted order, and only the edges inside the set {v1,…,vi} are known when the ...
I. Schiermeyer, Zs. Tuza, Margit Voigt
openaire +2 more sources