# Combinatorics and Graph Theory

## 1308 Submissions

[2] **viXra:1308.0037 [pdf]**
*submitted on 2013-08-06 19:55:15*

### Smarandache Multi-Spaces & Combinatorial Mathematics

**Authors:** Linfan Mao

**Comments:** 73 Pages.

A Smarandache multi-space is a union of n different spaces
equipped with some different structures, for an integer n≧2.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1308.0030 [pdf]**
*submitted on 2013-08-05 21:42:13*

### Estrada Index of Graphs

**Authors:** Mohammed Kasim, Fumao Zhang, Qiang Wang

**Comments:** 6 Pages.

Suppose $G$ is a simple graph. The eigenvalues $\delta_1,
\delta_2,\ldots, \delta_n$ of $G$ are the eigenvalues of its
adjacency matrix $A$. The Estrada index of the graph $G$ is defined
as $EE = EE(G) = \Sigma_{i=1}^{n} e^{\delta_i}$. In this paper the
basic properties of $EE$ are investigated. Moreover, some lower and
upper bounds for the Estrada index in terms of the number of
vertices, edges and the Randic index are obtained. In addition, some
relations between $EE$ and graph energy $E(G)$ are presented.

**Category:** Combinatorics and Graph Theory