EBSCO Logo
Connecting you to content on EBSCOhost
Results
Title

ON THE GRAPHS WITH DISTINGUISHING NUMBER EQUAL LIST DISTINGUISHING NUMBER.

Authors

ALIKHANI, S.; SOLTANI, S.

Abstract

The distinguishing number D(G) of a graph G is the least integer d such that G has a vertex labeling with d labels that is preserved only by the trivial automorphism. A list assignment to G is an assignment L = {L(v)} v∈V (G) of lists of labels to the vertices of G. A distinguishing L-labeling of G is a distinguishing labeling of G where the label of each vertex v comes from L(v). The list distinguishing number of G, denoted by Dl(G), is the minimum k such that every list assignment to G in which |L(v)| = k for all v ∈ V (G) yields a distinguishing L-labeling of G. In this paper, we determine the list-distinguishing number for two families of graphs. We also characterize all graphs with the distinguishing number equal the list distinguishing number. Finally, we show that this characterization works for other list numbers of a graph.

Subjects

GRAPH theory; INTEGERS; NUMBER theory; GEOMETRIC vertices; AUTOMORPHISMS; GRAPH labelings

Publication

Journal of Mahani Mathematical Research Center, 2023, Vol 12, Issue 2, p411

ISSN

2251-7952

Publication type

Academic Journal

DOI

10.22103/jmmr.2023.20163.1333

EBSCO Connect | Privacy policy | Terms of use | Copyright | Manage my cookies
Journals | Subjects | Sitemap
© 2025 EBSCO Industries, Inc. All rights reserved