On square difference graphs

In graph theory number labeling problems play vital role. Let G = (V, E) be a (p, q)-graph with vertex set V and edge set E. Let f be a vertex valued bijective function from V (G) → {0, 1, ..., p - 1}. An edge valued function f can be defined on G as a function of squares of vertex values. Graphs wh...

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Bibliographic Details
Published in:International journal of mathematical combinatorics 2012-03, Vol.1, p.31
Main Authors: V., Ajitha, Princy, K.L, Lokesha, V, Ranjini, P.S
Format: Article
Language:English
Subjects:
Functional equations
Functions
Graph theory
Graphs
Labeling
Social research
Studies
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Summary:In graph theory number labeling problems play vital role. Let G = (V, E) be a (p, q)-graph with vertex set V and edge set E. Let f be a vertex valued bijective function from V (G) → {0, 1, ..., p - 1}. An edge valued function f can be defined on G as a function of squares of vertex values. Graphs which satisfy the injectivity of this type of edge valued functions are called square graphs. Square graphs have two major divisions: they are square sum graphs and square difference graphs. In this paper we concentrate on square difference or SD graphs. An edge labeling f* on E(G) can be defined as follows. f* (uv) = |[(f(u)).sup.2] -[(f(v)).sup.2]| for every uv in E(G). If f* is injective, then the labeling is said to be a SD labeling. A graph which satisfies SD labeling is known as a SD graph. We illuminate some of the results on number theory into the structure of SD graphs. Also, established some classes of SD graphs and established that every graph can be embedded into a SD graph. Key Words: SD labeling, SD graph, strongly SD graph, perfect SD graph. AMS(2010): 05C20
ISSN:1937-1055
1937-1047