Distinguishing number and adjacency properties
نویسندگان
چکیده
منابع مشابه
The relationship between the distinguishing number and the distinguishing index with detection number of a graph
This article has no abstract.
متن کاملDistinguishing number and distinguishing index of natural and fractional powers of graphs
The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial automorphism. For any $n in mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...
متن کاملDistinguishing Edge Chromatic Number
An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15
متن کاملThe Distinguishing Chromatic Number
In this paper we define and study the distinguishing chromatic number, χD(G), of a graph G, building on the work of Albertson and Collins who studied the distinguishing number. We find χD(G) for various families of graphs and characterize those graphs with χD(G) = |V (G)|, and those trees with the maximum chromatic distingushing number for trees. We prove analogs of Brooks’ Theorem for both the...
متن کاملWell-quasi-ordering and finite distinguishing number
Balogh, Bollobás and Weinreich showed that a parameter that has since been termed the distinguishing number can be used to identify a jump in the possible speeds of hereditary classes of graphs at the sequence of Bell numbers. We prove that every hereditary class that lies above the Bell numbers and has finite distinguishing number contains a boundary class for well-quasi-ordering. This means t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2010
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2010.v1.n2.a4