23 citations · 62 across the 16 of their papers we have counts for
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On the Total Graph of a Finite Commutative Ring
Mohammad Hadi Shekarriz, Mohammad Hasan Shirdareh Haghighi, Habib Sharif
Let be a finite commutative ring with . In this article, we study the total graph of , denoted by , determine some of its basic graph-theoretical properties, d…
A Characterization For 2-Self-Centered Graphs
Mohammad Hadi Shekarriz, Madjid Mirzavaziri, Kamyar Mirzavaziri
A Graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered gra…
Bounds for Distinguishing Invariants of Infinite Graphs
Wilfried Imrich, Rafał Kalinowski, Monika Pilśniak +1
We consider infinite graphs. The distinguishing number of a graph is the minimum number of colours in a vertex colouring of that is preserved only by the trivial aut…
The Cost of Edge-distinguishing of the Cartesian Product of Connected Graphs
Aleksandra Gorzkowska, Mohammad Hadi Shekarriz
A graph is said to be -distinguishable if there is a vertex coloring of with a set of colors which breaks all of the automorphisms of but the identity. We call t…
Number of Distinguishing Colorings and Partitions
Bahman Ahmadi, Fatemeh Alinaghipour, Mohammad Hadi Shekarriz
A vertex coloring of a graph is called distinguishing (or symmetry breaking) if no non-identity automorphism of preserves it, and the distinguishing number, shown by …