TY - JOUR

T1 - The edge-graceful spectra of connected bicyclic graphs without pendant

AU - SHIU, Wai Chee

AU - Ling, M. H.

AU - Low, Richard M.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2008/8

Y1 - 2008/8

N2 - Let G be a connected simple (p, q)-graph and k a non-negative integer. The graph G is said to be k-edge-graceful if the edges can be labeled with k, k + 1,..., k + q - 1 so that the vertex sums are distinct modulo p. The set of all k where G is k-edge-graceful is called the edge-graceful spectrum of G. In 2004, Lee, Cheng and Wang analyzed the edge-graceful spectra of certain connected bicyclic graphs, leaving some cases as open problems. Here, we determine the edge-graceful spectra of all connected bicyclic graphs without pendant.

AB - Let G be a connected simple (p, q)-graph and k a non-negative integer. The graph G is said to be k-edge-graceful if the edges can be labeled with k, k + 1,..., k + q - 1 so that the vertex sums are distinct modulo p. The set of all k where G is k-edge-graceful is called the edge-graceful spectrum of G. In 2004, Lee, Cheng and Wang analyzed the edge-graceful spectra of certain connected bicyclic graphs, leaving some cases as open problems. Here, we determine the edge-graceful spectra of all connected bicyclic graphs without pendant.

UR - http://www.scopus.com/inward/record.url?scp=70349455976&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70349455976

VL - 66

SP - 171

EP - 185

JO - Journal of Combinatorial Mathematics and Combinatorial Computing

JF - Journal of Combinatorial Mathematics and Combinatorial Computing

SN - 0835-3026

ER -