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SWATI NAYAK,SHANKAR UPADHYAY,SABITHA D’SOUZA,PRADEEP G. BHAT 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.4
Let A(G) be the adjacency matrix of a graph G. Let s(v) denote the row entries of A(G) corresponding to the vertex v of G. 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 study the Hamming distance between the strings generated by the adjacency matrix of generalised complements of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of GPk and GP k(i).
Energy of partial complements of a graph
SWATI NAYAK,SABITHA DSOUZA,GOWTHAM H. J.,PRADEEP G. BHAT 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
The partial complement of a graph G with respect to a set S denoted by G S is the graph obtained by removing the edges of hSi and adding edges which are not in hSi in G. In this paper we introduce the concept of energy of partial complements of graph and partial complement energy is computed for few classes of graphs. Some bounds are obtained for partial complement energy of a graph G.
LABEL INCIDENCE ENERGY OF PARTIAL EDGE LABELED GRAPH
SABITHA D’SOUZA,GOWTHAM H. J.,SWATI NAYAK,PRADEEP G. BHAT 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.1
Let G = (V,E) be a simple graph with vertex set V = fv1, v2, . . . , vng and edge set E = fe1, e2, . . . , emg. The label incidence matrix Bl(G) of G is the n m matrix whose (i, j)-entry is a if 0 la- beled edge incident to 0 labeled vertex, b if 1 labeled edge incident to 1 labeled vertex, c if unlabeled edge incident to 0 or 1 labeled vertex and 0 otherwise. The label incidence energy IEl(G) is the sum of the singular values of Bl(G). In this paper we give lower and upper bounds for IEl(G) in terms of graph parameters and we study label incidence energy of some families of graph.