<abstract xmlns="http://www.w3.org/1999/xhtml">Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective function f : V(G) → P(ℕ0) such that the induced function f+ : E(G) → 𝒫(ℕ0) defined by f+(uv) = f(u) + f(v) is also injective. An IASI f is said to be a weak IASI if |f+(uv)| = max(|f(u)|, |f(v)|) for all u, v ∈ V(G). A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph G is the minimum number of edges with singleton set-labels, required for a graph G to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their corresponding sparing numbers.</abstract>

Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective function f : V(G) → P(ℕ0) such that the induced function f+ : E(G) → 𝒫(ℕ0) defined by f+(uv) = f(u) + f(v) is also injective. An IASI f is said to be a weak IASI if |f+(uv)| = max(|f(u)|, |f(v)|) for all u, v ∈ V(G). A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph G is the minimum number of edges with singleton set-labels, required for a graph G to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their corresponding sparing numbers.

The sparing number of certain graph powers

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The sparing number of certain graph powers"}

Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective...

The sparing number of certain graph powers

Published Online: Aug 17, 2019

Page range: 186 - 202

Received: Sep 07, 2018

DOI: https://doi.org/10.2478/ausm-2019-0015

Keywords
graph powers, integer additive set-indexers, weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph

© 2019 N. K. Sudev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The sparing number of certain graph powers

Published Online: Aug 17, 2019

Page range: 186 - 202

Received: Sep 07, 2018

DOI: https://doi.org/10.2478/ausm-2019-0015

Keywordsgraph powers, integer additive set-indexers, weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph

© 2019 N. K. Sudev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
graph powers, integer additive set-indexers, weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph