On the packing chromatic number of Moore graphs
نویسندگان
چکیده
The packing chromatic number ??(G) of a graph G is the smallest integer k for which there exists vertex coloring ?:V(G)?{1,2,…,k} such that any two vertices color i are at distance least i+1. For g?{6,8,12}, (q+1,g)-Moore graphs (q+1)-regular with girth g incidence symmetric generalized g?2-gons order q. In this paper we study G. g=6 present exact value ??(G). g=8, determine in terms intersection certain structures quadrangles. g=12, lower and upper bounds invariant when q?9 an odd prime power.
منابع مشابه
On Open Packing Number of Graphs
In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملPacking Chromatic Number of Distance Graphs
The packing chromatic number (G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X1; :::; Xk where vertices in Xi have pairwise distance greater than i. We study the packing chromatic number of in nite distance graphs G(Z; D), i.e. graphs with the set Z of integers as vertex set and in which two distinct vertices i; j 2 Z are adjacent if a...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملOn packing chromatic number of subcubic outerplanar graphs
The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the weak ...
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: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2020.10.009