Minimal k-rankings for prism graphs
نویسندگان
چکیده
We determine rank numbers for the prism graph P 2 ×C n (P 2 being the connected two-node graph and C n a cycle of length n) and for the square of an even cycle.
منابع مشابه
$4$-Total prime cordial labeling of some cycle related graphs
Let $G$ be a $(p,q)$ graph. Let $f:V(G)to{1,2, ldots, k}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $left|t_{f}(i)-t_{f}(j)right|leq 1$, $i,j in {1,2, cdots,k}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labelled with $x$. A graph with a $k$-total prime cordi...
متن کامل$Z_k$-Magic Labeling of Some Families of Graphs
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic} if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k...
متن کاملEnumeration of minimal 3D polyominoes inscribed in a rectangular prism
We consider the family of 3D minimal polyominoes inscribed in a rectanglar prism. These objects are polyominos and so they are connected sets of unitary cubic cells inscribed in a given rectangular prism of size b×k×h and of minimal volume equal to b + k + h − 2. They extend the concept of minimal 2D polyominoes inscribed in a rectangle studied in a previous work. Using their geometric structur...
متن کاملThe birank number of ladder, prism and Mobius ladder graphs
Given a graph G, a function f : V (G)→ {1, 2, ..., k} is a k-biranking of G if f(u) = f(v) implies every u-v path contains vertices x and y such that f(x) > f(u) and f(y) < f(u). The birank number of a graph, denoted bi(G), is the minimum k such that G has a k-biranking. In this paper we determine the birank numbers for ladder, prism, and Möbius ladder graphs.
متن کاملCohen-Macaulay $r$-partite graphs with minimal clique cover
In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010