TY - JOUR
ID - 359
TI - ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Alikhani, S.
AU - Jahari, S.
AD - Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
Y1 - 2015
PY - 2015
VL - 2
IS - 2
SP - 97
EP - 108
KW - Edge cover polynomial
KW - edge covering
KW - equivalence class
KW - cubic graph
KW - corona
DO - 10.22044/jas.2015.359
N2 - Let $G$ be a simple graph of order $n$ and size $m$. The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$, where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we study the edge cover polynomials of cubic graphs of order $10$. We show that all cubic graphs of order $10$ (especially the Petersen graph) are determined uniquely by their edge cover polynomials.
UR - https://jas.shahroodut.ac.ir/article_359.html
L1 - https://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf
ER -