A Classification of Semisymmetric Cubic Graphs of Order 28p&sup2

A graph is said to be semisymmetric if its full automorphism group actstransitively on its edge set but not on its vertex set. In this paper, we prove thatthere is only one semisymmetric cubic graph of order 28p<sub>2</sub>, where p is a prime.DOI : http://dx.doi.org/10.22342/jims.16.2.38.139-14

Perfect 3-colorings of the Cubic Graphs of Order 10

Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts A_1, A_2, ..., A_m such that, for all $i,j \in \lbrace 1, ... , m \rbrace$, every vertex of A_i is adjacent to the same number of vertices, namely, a_{ij} vertices, of A_j. The matrix $A=(a_{ij})_{i,j\in \lbrace 1,... ,m\rbrace }$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the cubic graphs of order 10. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 10

Perfect 3-Colorings of the Petersen‎ Graph

‎In this paper we enumerate the parameter matrices of all perfect 3-colorings of the Petersen graph‎