On Sufficient Conditions for Hamiltonicity in Dense Graphs

Sufficient Spectral Conditions for Hamiltonicity

The question of deciding whether or not a given graph is Hamiltonian is a very difficult one; indeed, determining whether a given graph is Hamiltonian is NP-complete. Here, we discuss applications of spectral graph theory to this problem. In particular, we explore results by Fiedler and Nikiforov [2] regarding spectral conditions on the adjacency matrix to ensure Hamiltonicity, and results by B...

Sufficient conditions for Hamiltonicity in multiswapped networks

OTIS networks are interconnection networks amenable to deployment as hybrid networks containing both electronic and optical links. Deficiencies as regards symmetry led to the subsequent formulation of biswapped networks which were later generalized to multiswapped networks so as to still enable optoelectronic implementation (as it happens, multiswapped networks also generalize previously studie...

A sufficient condition for Hamiltonicity in locally finite graphs

Using topological circles in the Freudenthal compactification of a graph as infinite cycles, we extend to locally finite graphs a result of Oberly and Sumner on the Hamiltonicity of finite graphs. This answers a question of Stein, and gives a sufficient condition for Hamiltonicity in locally finite graphs.

A clique-covering sufficient condition for hamiltonicity of graphs

On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs

Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either E...