Results 41 to 50 of about 587 (90)
Rainbow connection in $3$-connected graphs [PDF]
, 2010 An edge-colored graph $G$ is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are needed in ...
Li, Xueliang, Shi, Yongtang
core
Highly connected orientations from edge-disjoint rigid subgraphs
Forum of Mathematics, PiWe give an affirmative answer to a long-standing conjecture of Thomassen, stating that every sufficiently highly connected graph has a k-vertex-connected orientation. We prove that a connectivity of order $O(k^2)$ suffices.
Dániel Garamvölgyi +3 more
doaj +1 more source
The Super-Connectivity of Kneser Graphs
Discussiones Mathematicae Graph Theory, 2019 A vertex cut of a connected graph G is a set of vertices whose deletion disconnects G. A connected graph G is super-connected if the deletion of every minimum vertex cut of G isolates a vertex.
Ekinci Gülnaz Boruzanli +1 more
doaj +1 more source
On Conditional Connectivity of the Cartesian Product of Cycles
Discussiones Mathematicae Graph Theory, 2023 The conditional h-vertex (h-edge) connectivity of a connected graph H of minimum degree k > h is the size of a smallest vertex (edge) set F of H such that H − F is a disconnected graph of minimum degree at least h. Let G be the Cartesian product of r ≥ 1
Saraf J.B., Borse Y.M., Mundhe Ganesh
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
Fixed Points for Banach and Kannan Contractions in Modular Spaces with a Graph [PDF]
, 2013 In this paper, we discuss the existence and uniqueness of fixed points for Banach and Kannan $\widetilde G$-$\rho$-contractions defined on modular spaces endowed with a graph without using the $\Delta_2$-condition or the Fatou property.Comment: 12 ...
Aghanians, Aris, Nourouzi, Kourosh
core
Characterizing Atoms that Result from Decomposition by Clique Separators
Discussiones Mathematicae Graph Theory, 2017 A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition.
McKee Terry A.
doaj +1 more source
The generalized 3-connectivity of burnt pancake graphs and godan graphs
AKCE International Journal of Graphs and Combinatorics, 2023 The generalized k-connectivity of a graph G, denoted by [Formula: see text] is the minimum number of internally edge disjoint S-trees for any [Formula: see text] and [Formula: see text] The generalized k-connectivity is a natural extension of the ...
Jing Wang, Zuozheng Zhang, Yuanqiu Huang
doaj +1 more source
The Double Roman Domatic Number of a Digraph
Discussiones Mathematicae Graph Theory, 2020 A double Roman dominating function on a digraph D with vertex set V (D) is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function f : V (D) → {0, 1, 2, 3} having the property
Volkmann Lutz
doaj +1 more source
On minimum algebraic connectivity of graphs whose complements are bicyclic
Open Mathematics, 2019 The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model ...
Liu Jia-Bao +3 more
doaj +1 more source