Hamming graphs are, by definition, the Cartesian product of complete graphs. In the bipartite case these graphs are hypercubes. We present an algorithm recognizing Hamming graphs in linear time and space. This improves a previous algorithm which was linear in time but not in space. This also favorably compares to the general decomposition algorithms of graphs with respect to the Cartesian produ...

Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra and D. Basavayya [5]. In this paper we discuss s...

let g be a simple connected graph. the first and second zagreb indices have been introducedas  vv(g)(v)2 m1(g) degg and m2(g)  uve(g)degg(u)degg(v) , respectively,where degg v(degg u) is the degree of vertex v (u) . in this paper, we define a newdistance-based named hyperzagreb as e uv e(g) .(v))2 hm(g)     (degg(u)  degg inthis paper, the hyperzagreb index of the cartesian product...

The game chromatic number χg is considered for the Cartesian product G 2 H of two graphs G and H. We determine exact values of χg(G2H) when G and H belong to certain classes of graphs, and show that, in general, the game chromatic number χg(G2H) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is proved for the game coloring number colg(G2...

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product graphs and compute the Y new related to join graphs.