On resolving edge colorings in graphs.
Conditional resolvability in graphs: a survey.
Measures of traceability in graphs.
Weak solutions to a nonlinear variational wave equation and some related problems
In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the Young measure theory and related compactness results, in the first section. Then we use the Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second section....
On -strong distance in strong digraphs
For a nonempty set of vertices in a strong digraph , the strong distance is the minimum size of a strong subdigraph of containing the vertices of . If contains vertices, then is referred to as the -strong distance of . For an integer and a vertex of a strong digraph , the -strong eccentricity of is the maximum -strong distance among all sets of vertices in containing . The minimum -strong eccentricity among the vertices of is its -strong radius and the maximum...
The hull number of an oriented graph.
Hybrid viscosity iterative method for fixed point, variational inequality and equilibrium problems.
A class of Fan-Browder type fixed-point theorems and its applications in topological spaces.
Vehicle vibration analysis in changeable speeds solved by pseudoexcitation method.
On k-Path Pancyclic Graphs
For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic. In this paper, we present sufficient conditions for graphs to be k-path pancyclic. For a graph G of order n ≥ 3, we establish sharp lower bounds in terms of n and k for (a) the minimum degree of G, (b) the minimum degree-sum of nonadjacent vertices of G and (c) the size of G such that G...
On Closed Modular Colorings of Trees
Two vertices u and v in a nontrivial connected graph G are twins if u and v have the same neighbors in V (G) − {u, v}. If u and v are adjacent, they are referred to as true twins; while if u and v are nonadjacent, they are false twins. For a positive integer k, let c : V (G) → Zk be a vertex coloring where adjacent vertices may be assigned the same color. The coloring c induces another vertex coloring c′ : V (G) → Zk defined by c′(v) = P u∈N[v] c(u) for each v ∈ V (G), where N[v] is the closed neighborhood...
On graphs with a unique minimum hull set
We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.
The forcing geodetic number of a graph
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u-v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u,v) for u, v ∈ S. A set S is a geodetic set if I(S) = V(G). A minimum geodetic set is a geodetic set of minimum cardinality and this cardinality is the geodetic number g(G). A subset T of a minimum geodetic set S is called a forcing subset for S if S is the unique minimum geodetic set containing T. The forcing geodetic...
On stratification and domination in graphs
A graph G is 2-stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class), where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v. An F-coloring of a graph is a red-blue coloring of the vertices of G in which every blue vertex v belongs to a copy of F rooted at v. The F-domination number is the minimum number of red vertices in an F-coloring of G. In...
Connected partition dimensions of graphs
For a vertex v of a connected graph G and a subset S of V(G), the distance between v and S is d(v,S) = mind(v,x)|x ∈ S. For an ordered k-partition Π = S₁,S₂,...,Sₖ of V(G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v,S₁), d(v,S₂),..., d(v,Sₖ)). The k-partition Π is a resolving partition if the k-vectors r(v|Π), v ∈ V(G), are distinct. The minimum k for which there is a resolving k-partition of V(G) is the partition dimension pd(G) of G. A resolving partition Π = S₁,S₂,...,Sₖ...
Nowhere-zero modular edge-graceful graphs
For a connected graph G of order n ≥ 3, let f: E(G) → ℤₙ be an edge labeling of G. The vertex labeling f’: V(G) → ℤₙ induced by f is defined as , where the sum is computed in ℤₙ. If f’ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A modular edge-graceful labeling f of G is nowhere-zero if f(e) ≠ 0 for all e ∈ E(G) and in this case, G is a nowhere-zero modular edge-graceful graph. It is shown that a connected graph G of order n ≥ 3 is nowhere-zero...
Global solutions to vortex density equations arising from sup-conductivity
Weak solutions to a nonlinear variational wave equation with general data
On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation
Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle
In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches
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