PI index for some special graphs
ABSTRACT:
The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. Each structural feature of such organic molecule can be expressed as a graph. In this paper, we study the PI indices for some special graphs, such as Ir(Fn), Ir(Wn), ~ n F , ~ W n , Ir( ~ n F ) and Ir( ~ W n ).
INTRODUCTION
Wiener index (W) and Szeged index (Sz) are introduced to reflect certain structural features of organic molecules [1, 2]. Khadikar et al. [3, 4] introduced another index called Padmaker-Ivan (PI) index. For the previous results on PI index, can refer [5-8]. In this paper, we study the PI index of several simple connected graphs. The PI index of a graph G is defined as follows: PI=PI(G)= { ( | ) ( | )} eu ev n e G n e G , where e=uv, ( | ) eu n e G is the number of edges of G lying closer to u than v, ( | ) ev n e G is the number of edges of G lying closer to v than u and the summation goes over all edges of G. The edges which are equidistant from u and v are not considered for the calculation of PI index. In what follows, we write neu instead of ( | ) eu n e G for short. The readers can refer to [9] for standard graph theoretic concepts and terms used but undefined in this paper. In this paper, we determine the PI index for some special graphs. The organization of rest paper is as follows. First, we give some necessary definition in the next section. Then, the main result in this article is given in the third section.
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The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. Each structural feature of such organic molecule can be expressed as a graph. In this paper, we study the PI indices for some special graphs, such as Ir(Fn), Ir(Wn), ~ n F , ~ W n , Ir( ~ n F ) and Ir( ~ W n ).
INTRODUCTION
Wiener index (W) and Szeged index (Sz) are introduced to reflect certain structural features of organic molecules [1, 2]. Khadikar et al. [3, 4] introduced another index called Padmaker-Ivan (PI) index. For the previous results on PI index, can refer [5-8]. In this paper, we study the PI index of several simple connected graphs. The PI index of a graph G is defined as follows: PI=PI(G)= { ( | ) ( | )} eu ev n e G n e G , where e=uv, ( | ) eu n e G is the number of edges of G lying closer to u than v, ( | ) ev n e G is the number of edges of G lying closer to v than u and the summation goes over all edges of G. The edges which are equidistant from u and v are not considered for the calculation of PI index. In what follows, we write neu instead of ( | ) eu n e G for short. The readers can refer to [9] for standard graph theoretic concepts and terms used but undefined in this paper. In this paper, we determine the PI index for some special graphs. The organization of rest paper is as follows. First, we give some necessary definition in the next section. Then, the main result in this article is given in the third section.
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