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Generalized connectivity of some total graphs
We study the generalized k -connectivity κ k ( G ) as introduced by Hager in 1985, as well as the more recently introduced generalized k -edge-connectivity λ
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On Sectional Newtonian Graphs
In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs....
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Betti Numbers of Some Circulant Graphs
Let o ( n ) be the greatest odd integer less than or equal to n . In this paper we provide explicit formulae to compute ℕ-graded Betti numbers of the...
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When a line graph associated to annihilating-ideal graph of a lattice is planar or projective
Let ( L ,∧, ∨) be a finite lattice with a least element 0. A G ( L ) is an annihilating-ideal graph of L in which the vertex set is the set of all...
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Proper connection number of bipartite graphs
An edge-colored graph G is proper connected if every pair of vertices is connected by a proper path. The proper connection number of a connected...
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Bounds for the number of meeting edges in graph partitioning
Let G be a weighted hypergraph with edges of size at most 2. Bollobás and Scott conjectured that G admits a bipartition such that each vertex class...
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4-cycle properties for characterizing rectagraphs and hypercubes
A (0, 2)-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of (0,...
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Order of the smallest counterexample to Gallai’s conjecture
In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Zamfirescu conjectured that the smallest...
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Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs
In this paper, the upper and lower bounds for the quotient of spectral radius (Laplacian spectral radius, signless Laplacian spectral radius) and the...
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Some results on the annihilator graph of a commutative ring
Let R be a commutative ring. The annihilator graph of R , denoted by AG( R ), is the undirected graph with all nonzero zero-divisors of R as vertex set,...
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Chromatic number and subtrees of graphs
Let G and H be two graphs. We say that G induces H if G has an induced subgraph isomorphic to H : A. Gyárfás and D. Sumner, independently, conjectured...
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Edit distance measure for graphs
In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for g ( n , l ), the biggest...
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Even factors with a bounded number of components in iterated line graphs
We consider even factors with a bounded number of components in the n-times iterated line graphs L n ( G ). We present a characterization of a simple...
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Nonempty intersection of longest paths in a graph with a small matching number
A maximum matching of a graph G is a matching of G with the largest number of edges. The matching number of a graph G , denoted by α ′( G ), is the...
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Bipartition of graph under degree constraints
Let G be a graph, let s be a positive integer, and let X be a subset of V ( G ). Denote δ ( X ) to be the minimum degree of the subgraph G [ X ] induced by X ....
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The primitive Boolean matrices with the second largest scrambling index by Boolean rank
The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A k ( A T ) k = J , where A T denotes the...
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Non-hyperbolicity in random regular graphs and their traffic characteristics
In this paper we prove that random d -regular graphs with d ≥ 3 have traffic congestion of the order O( n log
d−1 3 n ) where n is the number of nodes... -
Gromov hyperbolicity of planar graphs
We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a...
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Acyclic edge coloring of planar graphs without adjacent cycles
A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G . The acyclic edge chromatic number of G , denoted by χ ′ ...
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Pfaffian graphs embedding on the torus
An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G − V ( C ) has a perfect matching has an odd...