Graphs Isomorphisms Under Edge-Replacements and the Family of Amoebas

On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

On the edge and total GA indices of some graphs

Isomorphisms of P4-graphs

For graphs G and G' with minimum degree is = 3 and satisfying one of two other conditions, we prove that any isomorphism from the P4 -graph P4 (G) to P4 ( G') can be induced by a vertex-isomorphism of G onto G'. We also prove that a connected graph G is isomorphic to its P4 -graph P4 (G) if and only if G is a cycle of length at least 4.

Edge detection based on morphological amoebas

Detecting the edges of objects within images is critical for quality image processing. We present an edge-detecting technique that uses morphological amoebas that adjust their shape based on variation in image contours. We evaluate the method both quantitatively and qualitatively for edge detection of images, and compare it to classic morphological methods. Our amoeba-based edge-detection syste...

On the revised edge-Szeged index of graphs

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...