### Hamming index of graphs with respect to its incidence matrix

#### Abstract

*B*(

*G*) be the incidence matrix of a graph

*G*. The row in

*B*(

*G*)corresponding to a vertex

*v*, denoted by

*s*(

*v*) is the string which belongs to ℤ

^{m}

_{2}, a set of

*m*-tuples over a field of order two. The Hamming distance between the strings

*s*(

*u*) and

*s*(

*v*) is the number of positions in which

*s*(

*u*) and

*s*(

*v*) differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.19184/ijc.2022.6.2.4

#### References

A. B. Ganagi, H. S. Ramane, Hamming distance between the strings generated by adjacency matrix of a graph and their sum, *Algebra Discrete Math.*, **22** (2016), 82-93.

F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.

W. Imrich, S. Klavzar, A simple O(mn) algorithm for recognizing Hamming graphs, *Bull. Inst. Combin. Appl.*, **9** (1993), 45-56.

S. Klavzar, I. Peterin, Characterizing subgraphs of Hamming graphs, *J. Graph Theory*, **49** (2005), 302-312.

B. Kolman, R. Busby, S. C. Ross, Discrete Mathematical Structures, Prentice Hall of India, New Delhi, 2002.

H. S. Ramane, A. B. Ganagi, Hamming index of class of graphs, *Int. J. Curr. Engg. Tech.*, (2013), 205-208.

H. S. Ramane, V. B. Joshi, R. B. Jummannaver, V. V. Manjalapur, S. C. Patil, S. D. Shindhe, V. S. Hadimani, V. K. Kyalkonda, B. C. Baddi, Hamming index of a graph generated by an edge-vertex incidence matrix, *Int. J. Math. Sci. Engg. Appl.*, **9** (2015), 93-103.

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