PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS

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SHIU W.C.; KWONG H.

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Journal: TRANSACTIONS ON COMBINATORICS Year:2012 | Volume:1 | Issue:1 Page(s): 15-20

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Information Journal Paper

Title

PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS

Author(s)

SHIU W.C. | KWONG H. | Issue Writer Certificate

Keywords

FRIENDLY LABELINGQ2

FRIENDLY INDEX SETQ2

PRODUCT-CORDIAL INDEXQ2

PRODUCT-CORDIAL INDEX SETQ2

TORUSQ2

Abstract

Let G = (V,E) be a connected simple graph. A labeling f: ® Z2 induces two edge labelings f+, f*: E® Z2 defined by f+(xy) = f(x)+f(y) and f*(xy) = f(x)f(y) for each xyÎE. For iÎZ2, let vf (i)= |f-1(i)|, e f+ (i)= |(f+)-1(i)| and e f* (i) = |(f*)-1(i)|. A labeling f is called friendly if |vf (1)-vf (0)| £1. For a FRIENDLY LABELING f of a graph G, the friendly index of G under f is defined by if+ (G) = e f+(1) – e f+(0). The set {if+ (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 if*(G) = ef* (1) – ef* (0). The set {if* (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.

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APA: Copy

SHIU, W.C., & KWONG, H.. (2012). PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS. TRANSACTIONS ON COMBINATORICS, 1(1), 15-20. SID. https://sid.ir/paper/213758/en

Vancouver: Copy

SHIU W.C., KWONG H.. PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS. TRANSACTIONS ON COMBINATORICS[Internet]. 2012;1(1):15-20. Available from: https://sid.ir/paper/213758/en

IEEE: Copy

W.C. SHIU, and H. KWONG, “PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS,” TRANSACTIONS ON COMBINATORICS, vol. 1, no. 1, pp. 15–20, 2012, [Online]. Available: https://sid.ir/paper/213758/en

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