Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Transactions on Comb...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Transactions on Combinatorics
Article . 2012
Data sources: DOAJ
mEDRA
Article . 2012
Data sources: mEDRA
versions View all 3 versions
addClaim

Product-cordial index and friendly index of regular graphs

Authors: Shiu, Wai Chee; Harris, Kwong;

Product-cordial index and friendly index of regular graphs

Abstract

Let $G=(V,E)$ be a connected simple graph. A labeling $f:V to Z_2$ induces two edge labelings $f^+, f^*: E to Z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in E$. For $i in Z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. A labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. For a friendly labeling $f$ of a graph $G$, the friendly index of $G$ under $f$ is defined by $i^+_f(G) = e_{f^+}(1)-e_{f^+}(0)$. The set ${i^+_f(G) | f is a friendly labeling of G}$ is called the full friendly index set of $G$. Also, the product-cordial index of $G$ under $f$ is defined by $i^*_f(G) = e_{f^*}(1)-e_{f^*}(0)$. The set ${i^*_f(G) | f is a friendly labeling of G}$ is called the full product-cordial index set of $G$. In this paper, we find a relation between the friendly index and the product-cordial index of a regular graph. As applications, we will determine the full product-cordial index sets of torus graphs which was asked by Kwong, Lee and Ng in 2010; and those of cycles.

Related Organizations
Keywords

product-cordial index set, Friendly labeling, friendly index set, QA1-939, product-cordial index, torus, Mathematics

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold