In this paper, we study the relationships between graphs and prime spectrum of unitary commutative rings. It is shown that a graph G equipped with G-right topology satisfies some spectral properties. particular give necessarily sufficient condition to obtain graph.

This paper studies the Laplacian spectrum and average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is eigenvalues a large dense graph can be effectively approximated by using degree function corresponding graphon. More specifically, we show how to approximate distribution (Kirchhoff index) graph. For all cases, provide explicit bounds...

solvable graphs (also known as reachable graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). in this paper, the properties of solvable graphs are investigated, and a new concept in multi agent moti...

There are six classes of endomorphisms for a graph. The sets these form chain under the inclusion sets. In order to systematically study endomorphisms, Böttcher and Knauer defined concepts endomorphism spectrum type graph in 1992. this paper, based on property structure monoids graphs, double-edge fan graphs described. particular, we give spectra types graphs.

A set S of edge-disjoint hamilton cycles in a graph T is said to be maximal if the hamilton cycles in S form a subgraph of T such that T − E(S) has no hamilton cycle. The spectrum of a graph T is the set of integers m such that T contains a maximal set of m edge-disjoint hamilton cycles. This spectrum has previously been determined for all complete graphs, all complete bipartite graphs, and man...