
In this paper, we show that the independence polynomial
Let
We consider a variation of a classical Turán-type extremal problem due to Bollobás
The hyperbolic Fibonacci function, which is the continuous extension of Binet’s formula for the Fibonacci number, transforms the Fibonacci number theory into a “continuous” theory because every identity for the hyperbolic Fibonacci function has its discrete analogy in the framework of the Fibonacci number. In this new paper, we define three important generalizations of the
A new construction of authentication codes with arbitration from pseudo-symplectic geometry over finite fields is given. The parameters and the probabilities of deceptions of the codes are also computed.
It was conjectured in a recently published paper that for any integer
Inspired by a recent paper by Giulietti, Korchmàros and Torres
In this paper, we study the global behavior of the nonnegative equilibrium points of the difference equation
where
The chromatic polynomial of a graph
An
We provide the specifics of how affine planes of orders three, four, and five can be used to partition the full design comprising all triples on
In this paper, the notion of left-right and right-left
Let
We call the digraph
A set
(i) For every pair of different vertices
(ii) For every vertex
In this paper, it is proved that if
Some previous results are generalized.
Let
A graph is said to be cordial if it has a
We initiate a study of the toughness of infinite graphs by considering a natural generalization of that for finite graphs. After providing general calculation tools, computations are completed for several examples. Avenues for future study are presented, including existence problems for tough-sets and calculations of maximum possible toughness. Several open problems are posed.
Let an
Let
A vertex cut that separates the connected graph into components such that every vertex in these components has at least
A graph
For a graph
It is known that the number of Dyck paths is given by a Catalan number. Dyck paths are represented as plane lattice paths which start at the origin
Let
The eccentricity
This paper investigates the dihedral group as the array stabilizer of an augmented
A proper vertex coloring of a graph
The centro-polyhedral group
In this paper, we obtain the periods of
We study two-path convexity in bipartite tournaments. For a bipartite tournament, we obtain both a necessary condition and a sufficient condition on the adjacency matrix for its rank to be two. We then investigate 4-cycles in bipartite tournaments of small rank. We show that every vertex in a bipartite tournament of rank two lies on a four cycle, and bipartite tournaments with a maximum number of 4-cycles do not necessarily have minimum rank.
A set
Katerinis established the following result in [1]. Let
(1)
(2)
Then
A cosimple regular matroid
Suppose
Let
A
Improving on Domokos’s improvement of Swan’s theorem, we show that under certain conditions on a finite digraph, whenever
Double-loop networks have been widely studied as architecture for local area networks. A double-loop network
for some fixed steps
Ramanujan’s
A diagonalised lattice is a two dimensional grid, where we add exactly one arbitrary diagonal in each square, and color each vertex black or white.We show that for every diagonalised lattice there is a walk from the left to the right, using only black vertices, if and only if there is no walk from the top to the bottom, using only white vertices.
A terrace for
We determine the full Sylow
Let
Special issue: Proceedings of International Conference on Discrete Mathematics (ICDM 2025)
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