PC-Labeling of a Graph and its PC-Set
نویسنده
چکیده
Abstract A binary vertex labeling f : V (G) → Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f∗ : E(G) → Z2 defined by f∗(uv) = f(u)f(v) for all uv ∈ E(G). Let ef (i) = {uv ∈ E(G) : f∗(uv) = i} be the number of edges of G that are labeled i. Productcordial index of the labeling f is the number pc(f) = |ef (0)− ef (1)|. The product-cordial set of the graph G, denoted by PC(G), is defined by PC(G) = {pc(f) : f is a friendly labeling of G }.
منابع مشابه
Evaluation of the clearance characteristics of liposomes in the human nose by gamma-scintigraphy
The nasal cavity possesses many advantages as a site for drug delivery, such as, ease of administration, applicability for long term treatments and a large surface area for absorption. One important limiting factor for nasal drug delivery is the limited time available for absorption within the nasal cavity due to mucociliary clearance. Several drug delivery systems including different kinds of ...
متن کاملEvaluation of the clearance characteristics of liposomes in the human nose by gamma-scintigraphy
The nasal cavity possesses many advantages as a site for drug delivery, such as, ease of administration, applicability for long term treatments and a large surface area for absorption. One important limiting factor for nasal drug delivery is the limited time available for absorption within the nasal cavity due to mucociliary clearance. Several drug delivery systems including different kinds of ...
متن کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کاملConstructing Graceful Graphs with Caterpillars
A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...
متن کاملProduct Cordial Sets of Long Grids
A binary vertex coloring (labeling) f : V (G) → Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f∗ : E(G) → Z2 defined by f∗(uv) = f(u)f(v) for all uv ∈ E(G). Let ef (i) = |{uv ∈ E(G) : f∗(uv) = i}| be the number of edges of G that are labeled i. Product-cordial ind...
متن کامل