
A set
In 1991 Gnanajothi conjectured: Each tree is odd-graceful. In this paper, we define the edge-ordered odd-graceful labeling of trees and show the odd-gracefulness of all symmetric trees.
A method is suggested for the construction of quadrangulations of the closed orientable surface with given genus
For integers
In this paper, we give an alternative and more intuitive proof to one of two classic inequalities given by Diaconis and Graham in 1977. The inequality involves three metrics on the symmetric group, i.e., the set of all permutations of the first
Pooling designs are standard experimental tools in many biotechnical applications. In this paper, we construct a family of error-correcting pooling designs with the incidence matrix of two types of subspaces of singular linear space over finite fields, and exhibit their disjunct properties.
Let
Thus we obtain a finite family of staircase convex cones whose union is
If there are integers
for each edge
Let
Calculations of the number of equivalence classes of Sudoku boards has to this point been done only with the aid of a computer, in part because of the unnecessarily large symmetry group used to form the classes. In particular, the relationship between relabeling symmetries and positional symmetries such as row/column swaps is complicated. In this paper, we focus first on the smaller Shidoku case and show first by computation and then by using connectivity properties of simple graphs that the usual symmetry group can in fact be reduced to various minimal subgroups that induce the same action. This is the first step in finding a similar reduction in the larger Sudoku case and for other variants of Sudoku.
Let
for each vertex
The signed
for each
In this paper, we initiate the study of signed
A graceful
Let
In this paper, we introduce several concepts related to fuzzy algebraic structures. We provide an example of a fuzzy binary operation and a fuzzy group. Additionally, we define a new fuzzy binary operation on a
Let
In this paper, we obtain a lower bound as well as an upper bound for the domination number of
In view of these results, we conjecture that the domination number of
For given graphs
We show that if
A
An
In this paper, we investigate
A set of vertices
The subdivision of an edge
In this paper, we study domination critical graphs upon edge subdivision. We present several properties and bounds for these graphs and then give a constructive characterization of domination critical trees upon edge subdivision.
Let
A
Define an edge
We propose an original approach to the problem of rank-unimodality for Dyck lattices. It is based on a well-known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains. Even if we are not able to prove that Dyck lattices are rank-unimodal, we describe a family of polynomials (which constitutes a polynomial analog of ballot numbers) and a succession rule which appear to be useful in addressing such a problem. At the end of the paper, we also propose and begin a systematic investigation of the problem of unimodality of succession rules.
A Roman dominating function on a graph
In this paper, we initiate the study of the Roman fractional bondage number, and we present different bounds on Roman fractional bondage. In addition, we determine the Roman fractional bondage number of some classes of graphs.
We show that the principal results of the article “The metric dimension of graphs with pendant edges” [Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 139-145] do not hold. In this paper, we correct the results and we solve two open problems described in the above-mentioned paper.
Using the definition of the representation number of a graph modulo integers given by Erdős and Evans, we establish the representation number of a complete graph minus a set of disjoint stars. The representation number of a graph
Let
The decycling index of a digraph is the minimum number of arcs whose removal yields an acyclic digraph. The maximum arc decycling number
Let
1970-2025 CP (Manitoba, Canada) unless otherwise stated.