A graph G is pancyclic if it contains cycles of each length `, 3 ≤ ` ≤ |V (G)|. The generalized bull B(i, j) is obtained by associating one endpoint of each of the paths Pi+1 and Pj+1 with distinct vertices of a triangle. Gould, Luczak and Pfender [4] showed that if G is a 3-connected {K1,3, B(i, j)}-free graph with i + j = 4 then G is pancyclic. In this paper, we prove that every 4-connected, ...

The distance matrix of a simple graph G is D(G) = (di,j), where di,j is the distance between the ith and jth vertices of G. The greatest eigenvalue λ1 of D(G) is called the distance spectral radius of the graph G and is denoted by λ1(G). A simple connected graph G is called a 2-partite distance regular graph if there exists a partition V1 ∪V2 of the vertex set of G such that for i = 1, 2 and an...

In 1976, F. Loupekine created a method for constructing new snarks from already known ones. In the present work, we consider an infinite family of snarks constructed from the Petersen Graph using Loupekine’s method, and show that this family verifies Fulkerson’s Conjecture. In addition, we show that it is possible to extend this result to families constructed from snarks other than the Petersen...