شماره ركورد كنفرانس :
4062
عنوان مقاله :
PROOF OF A CONJECTURE ON THE DISTINGUISHING INDEX OF A GRAPH
پديدآورندگان :
ALIKHANI SAEID alikhani@yazd.ac.ir Department of Mathematics, Yazd University , SOLTANI SAMANEH s.soltani1979@gmail.com Department of Mathematics, Yazd University
كليدواژه :
Distinguishing index , Edge colourings , Symmetry breaking in graphs.
عنوان كنفرانس :
نهمين كنفرانس ملي نظريه گراف و تركيبيات جبري
چكيده فارسي :
The distinguishing index of a graph G, denoted by D
0
(G), is the least number
of labels in an edge labeling of G not preserved by any non-trivial automorphism. It was
conjectured by Pil´sniak (2015) that for any 2-connected graph D
0
(G) ≤ d p
Δ(G)e + 1.
We prove this conjecture. Furthermore, we propose a more general conjecture for upper
bound of D
0
(G).
