On a problem of R. Häggkvist concerning edge-colourings of graphs
On balancing of hypergraphs
On Complex Eigenvalues of M and P Matrices.
On cubic planar hypohamiltonian and hypotraceable graphs.
On eulerian irregularity in graphs
A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G is an Eulerian walk that encounters no two edges of G the same number of times. The minimum length of an...
On eulerian subgraphs of complementary graphs
On -closed graphs
On Hamiltonian circuits and spanning trees of hypercubes
On Hamiltonian consecutive-d digraphs
On Hamiltonian cycles in two-triangle graphs
On Hamiltonian cycles of complete -partite graphs
On hypergraphs of maximal simple paths of a class of Hamiltonian graphs
On hyper-Zagreb index conditions for hamiltonicity of graphs
During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to be Hamilton-connected....
On -ordered bipartite graphs.
On -path hamiltonian graphs and line-graphs
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 L-ideal-based L-zero-divisor graphs
In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.
On n-distant Hamiltonian line graphs.
On open Hamiltonian walks in graphs
On Partially Directed Eulerian Multigraphs