In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a vertex. The motivation of our study comes from the theory of non-ideal gases and, more specifically, from the virial equation of state. It is a known result o...

Graphs considered in this paper are simple finite undirected graphs without loops or multiple edges. A where each vertex has degree 3 is called cubic graphs. graphs, that is, 1-connected bridge graph traceable if its contains Hamiltonian path otherwise, non-traceable. In paper, we introduce a new family of Non-Traceable Cubic Bridge Graph (NTCBG) satisfy the conjecture Zoeram and Yaqubi (2017)....

In part (I) of this paper, it is proved that there are no limit points for the set of values of average genus of 2-connected simplicial graphs and of 3-connected graphs. The need for such restrictions is now demonstrated by showing that innnitely many real numbers are limit points of values of average genus for 2-connected non-simplicial graphs. A systematic method for constructing such limit p...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

We study the spectral radius of connected non-regular graphs. Let λ1(n,Δ) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degree Δ. We prove that Δ− λ1(n,Δ)=Θ(Δ/n). This improves two recent results by Stevanović and Zhang, respectively. © 2007 Elsevier Inc. All rights reserved.

We consider the class F of labelled 2-connected non-planar graphs without a K3,3-subdivision that are embeddable in the projective plane. A method of enumerating these graphs is described. We also enumerate the homeomorphically irreducible graphs in F and homeomorphically irreducible 2-connected planar graphs. The methods are based on the projective-planarity characterization for graphs without...