The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

A subset $C$ of the vertex set a graph $\Gamma$ is called perfect code if every at distance no more than one to exactly in $C$. Let $A$ be finite abelian group and $T$ square-free $A$. The Cayley sum with respect connection simple as its set, two vertices $x$ $y$ are adjacent whenever $x+y\in T$. subgroup said some In this paper, we give necessary sufficient conditions for given We also charact...

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...