TY - JOUR

T1 - Recognizing generalized Sierpiński graphs

AU - Imrich, Wilfried

AU - Peterin, Iztok

PY - 2020/4/1

Y1 - 2020/4/1

N2 - Let H be an arbitrary graph with vertex set V (H) = [nH] = {l,…, nH}. The generalized Sierpiński graph SnH , n ∈ N, is defined on the vertex set [nH]n, two different vertices u = un …u1 and v = vn … v1 being adjacent if there exists an h∈ [n] such that (a) ut = vt, for t > h, (b) uh ≠ vh and uhvh ∈ E(H), and (c) ut = vh and vt = uh for t < h. If H is the complete graph Kk, then we speak of the Sierpiński graph Sn k . We present an algorithm that recognizes Sierpiński graphs Sn k in O(|V (Sn k )|1+1=n) = O(|E(Sn k )|) time. For generalized Sierpiński graphs SnH we present a polynomial time algorithm for the case when H belong to a certain well defined class of graphs. We also describe how to derive the base graph H from an arbitrarily given SnH .

AB - Let H be an arbitrary graph with vertex set V (H) = [nH] = {l,…, nH}. The generalized Sierpiński graph SnH , n ∈ N, is defined on the vertex set [nH]n, two different vertices u = un …u1 and v = vn … v1 being adjacent if there exists an h∈ [n] such that (a) ut = vt, for t > h, (b) uh ≠ vh and uhvh ∈ E(H), and (c) ut = vh and vt = uh for t < h. If H is the complete graph Kk, then we speak of the Sierpiński graph Sn k . We present an algorithm that recognizes Sierpiński graphs Sn k in O(|V (Sn k )|1+1=n) = O(|E(Sn k )|) time. For generalized Sierpiński graphs SnH we present a polynomial time algorithm for the case when H belong to a certain well defined class of graphs. We also describe how to derive the base graph H from an arbitrarily given SnH .

KW - Algorithm

KW - Generalized sierpiński graphs

KW - Sierpiński graphs

UR - http://www.scopus.com/inward/record.url?scp=85092225064&partnerID=8YFLogxK

U2 - 10.2298/AADM180331003I

DO - 10.2298/AADM180331003I

M3 - Article

AN - SCOPUS:85092225064

VL - 14.2020

SP - 122

EP - 137

JO - Applicable analysis and discrete mathematics

JF - Applicable analysis and discrete mathematics

SN - 1452-8630

IS - 1

ER -