A. Alanazi

activity

20182026

most citedOn the Maximum Sigma Index of k-Cyclic Graphs

4 citations · 4 across the 7 of their papers we have counts for

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6 papers · 1 filter

math.CO2025

On the Diminished Sombor Index of Fixed-Order Molecular Graphs With Cyclomatic Number at Least 3

Abdulaziz Mutlaq Alotaibi, Abdulaziz M. Alanazi, Taher S. Hassan +1

For a graph $G$ with edge set $E$ , let $d (u)$ denote the degree of a vertex $u$ in $G$ . The diminished Sombor (DSO) index of $G$ is defined as $DSO(G)=\sum_{uv\in E}\sqrt{(d(u))^2+…

math.CO2025

Signed Partitions and Rogers-Ramanujan type Identities

Abdulaziz M. Alanazi, Augustine O. Munagi, Andrew V. Sills

George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561--573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where s…

math.CO2025

"Overpartitionized" Rogers--Ramanujan type identities

Abdulaziz Alanazi, Augustine O. Munagi, Andrew V. Sills

Many classical $q$ -series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically m…

math.CO2025

On a Conjecture Concerning the Complementary Second Zagreb Index

Hicham Saber, Tariq Alraqad, Akbar Ali +2

The complementary second Zagreb index of a graph $G$ is defined as $c M_{2} (G) = \sum_{uv \in E (G)} ∣ (d_{u} (G))^{2} - (d_{v} (G))^{2} ∣$ , where $d_{u} (G)$ denotes the degree of a vertex $u$ in $G$ and…

math.CO2023

Harmonic-Arithmetic Index of (Molecular) Trees

Abeer M. Albalahi, Akbar Ali, Abdulaziz M. Alanazi +2

Let $G$ be a graph. Denote by $d_{x}$ , $E (G)$ , and $D (G)$ the degree of a vertex $x$ in $G$ , the set of edges of $G$ , and the degree set of $G$ , respectively. This paper proposes to…

math.CO2022★ 4 cited

On the Maximum Sigma Index of k-Cyclic Graphs

Akbar Ali, Abeer M. Albalahi, Abdulaziz M. Alanazi +2

Let $G$ be a graph with edge set $E (G)$ . Denote by $d_{w}$ the degree of a vertex $w$ of $G$ . The sigma index of $G$ is defined as $\sum_{uv \in E (G)} (d_{u} - d_{v})^{2}$ . A connected graph o…