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Bounds and color energy of derived graphs
GOWTHAM H. J.,SABITHA DSOUZA,PRADEEP G. BHAT 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.2
Let G be a nite connected simple graph. The color energy of a graph G is dened as the sum of absolute values of color eigenvalues of G. The derived graph of a simple graph G, denoted by Gy, is a graph having same vertex set as G, in which two vertices are adjacent if and only if their distance in G is two. In this paper, we establish an upper and lower bounds for color energy of a graph and obtain color energy of derived graphs of some families of graphs.
Degree distance index of generalized complements of graphs
A. Harshitha,H. J. Gowtham,D'Souza Sabitha,G. Bhat Pradeep 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.1
Degree distance index of generalized complements of graphs
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.
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.